Recent developments in magnetocaloric materials - Portugalmagnetocaloric.web.ua.pt/files/rpp5_6_R04.pdf · Recent developments in magnetocaloric materials ... direct versus indirect

INSTITUTE OF PHYSICS PUBLISHING REPORTS ON PROGRESS IN PHYSICS

Rep. Prog. Phys. 68 (2005) 1479–1539 doi:10.1088/0034-4885/68/6/R04

Recent developments in magnetocaloric materials

K A Gschneidner Jr1,2,3, V K Pecharsky1,2 and A O Tsokol1

1 Materials and Engineering Physics Program, Ames Laboratory, Iowa State University,Ames, IA 50011-3020, USA2 Department of Materials Science and Engineering, Iowa State University, Ames,IA 50011-2300, USA

E-mail: [email protected]

Received 7 October 2004, in final form 17 March 2005Published 20 May 2005Online at stacks.iop.org/RoPP/68/1479

Abstract

The recent literature concerning the magnetocaloric effect (MCE) has been reviewed. The MCEproperties have been compiled and correlations have been made comparing the behavioursof the different families of magnetic materials which exhibit large or unusual MCE values.These families include: the lanthanide (R) Laves phases (RM2, where M = Al, Co and Ni),Gd5(Si1−xGex)4, Mn(As1−xSbx), MnFe(P1−xAsx), La(Fe13−xSix) and their hydrides and themanganites (R1−xMxMnO3, where R = lanthanide and M = Ca, Sr and Ba). The potentialfor use of these materials in magnetic refrigeration is discussed, including a comparison withGd as a near room temperature active magnetic regenerator material.

(Some figures in this article are in colour only in the electronic version)

3 Author to whom any correspondence should be addressed.

0034-4885/05/061479+61$90.00 © 2005 IOP Publishing Ltd Printed in the UK 1479

http://dx.doi.org/10.1088/0034-4885/68/6/R04

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1480 K A Gschneidner et al

Contents

Page1. Introduction 14822. Theory 14833. Elements and their solid solutions 14864. Binary and ternary intermetallic compounds 1487

4.1. Laves phases 14874.2. Miscellaneous intermetallic compounds 1491

5. Gd5(Si1−xGex)4 and related 5 : 4 materials 14955.1. General comments 14955.2. Gd5(Si1−xGex)4 alloys 14975.3. Other R5(Si1−xGex)4 systems 14995.4. Sn containing R5T4 compounds 1500

6. Mn-based compounds 15016.1. Mn(As1−xSbx) alloys 15016.2. MnFe(P1−xAsx) alloys 15026.3. Ni–Mn–Ga Heusler alloys 15036.4. Miscellaneous compounds 1504

7. La(Fe13−xMx)-based compounds 15067.1. Unsubstituted La(Fe13−xSix) 15067.2. Mossbauer and neutron diffraction studies 15097.3. Substitution for La 15097.4. Substitution for Fe 15097.5. Addition of interstitial elements—hydrogen 15107.6. Addition of interstitial elements—carbon 15117.7. Direct measurement of MCE 15127.8. La(Fe13−xAlx)-based alloys 1512

8. Manganites 15138.1. (La1−xMx)MnO3 where M = Na and Ag 15138.2. (La1−xCax)MnO3 15138.3. (R1−xSrx)MnO3 15168.4. Charge Order 15168.5. (La1−xBax)MnO3 15178.6. (La1−xMx)3Mn2O7 1518

9. Nanocomposites 151810. Correlations 1520

10.1. Adiabatic temperature rise: direct versus indirect measurements 152010.2. The lattice entropy 152110.3. The magnetic field dependence of the MCE 152210.4. The temperature dependence of the MCE 152210.5. The relationship between the magnetoresistance and the MCE 1524

11. Magnetic refrigeration 152411.1. Magnetic refrigerators 1524

Recent developments in magnetocaloric materials 1481

11.2. Thermodynamic cycles 152611.3. Regenerator materials 152811.4. Permanent magnet arrays 1533

12. Conclusions and summary 1533Acknowledgments 1533References 1533


1. Introduction

Many events related to the coupling of magnetic sublattices with an external magnetic field canbe triggered by varying the latter around a solid. This includes the magneto-thermodynamicphenomenon known as the magnetocaloric effect (MCE), which in a way resembles processesthat occur in a gas in response to the changing pressure. In a gaseous system, positional disorderand, therefore, the corresponding component of the entropy are suppressed during isothermalcompression. Similarly, isothermal magnetizing of a paramagnetic solid near absolute zeroor a ferromagnetic material near its spontaneous magnetic ordering temperature—the Curietemperature, TC—greatly reduces the disorder of a spin system, thus substantially loweringthe magnetic part of the total entropy. In the reverse process, which is similar to the expansionof a gas at constant temperature, isothermal demagnetizing restores the zero field magneticentropy of a system. These transformations of a solid can be quantified by means of an extensiveparameter representing the MCE—the isothermal magnetic entropy change, �SM. When agas is compressed adiabatically, its total entropy remains constant, whereas the velocities ofthe constituent molecules and, therefore, the temperature of the gas both increase. Likewise,the sum of the lattice and electronic entropies of a solid must change by the opposite of �SM

as a result of adiabatically magnetizing (or demagnetizing) the material, thus resulting in anincrease (decrease) of the lattice vibrations and the adiabatic temperature change, �Tad, whichis an intensive thermodynamic quantity also used to measure and express the MCE.

Although the MCE was discovered in 1881 [1], the first major advance occurred in the late1920s when cooling via adiabatic demagnetization was independently proposed by Debye [2]and Giauque [3]. The process was demonstrated for the first time in the history of physics a fewyears later when Giauque and MacDougall in 1933 [4] reached 0.25 K. Between 1933 and 1997,a number of advances in utilization of the MCE for cooling occurred (these have been describedin recent reviews [5–8]). However, two major developments occurred in 1997. The first wasthe February 20, 1997 unveiling of a proof-of-principle magnetic refrigerator demonstratingthat magnetic refrigeration is a viable and competitive cooling technology in the near roomtemperature region [9] with potential energy savings of up to 30%. In addition, magneticrefrigeration is an environmentally friendly technology since it eliminates ozone depletinggases, reduces the need for global warming greenhouse effect gases, and other hazardousgaseous refrigerants. The second breakthrough was the announcement of the discovery ofthe giant MCE (GMCE) in Gd5(Si2Ge2) on June 9, 1997 [10]. The details of these twobreakthroughs and the resultant flurry of research activities4 that occurred up to 2000 havebeen summarized in a number of reviews [5–8] and [11–13] and will not be repeated here.This review will be primarily concerned with the developments that have taken place since1 January 2000 and 1 September 2004.

Most authors report the MCE as �SM using the units of J kg−1K−1, but other units arealso used (J mol−1 K−1 and mJ cm−3 K−1). Usually the same authors note their materialswould be useful magnetic refrigerants and compare them with selected prototype materials;unfortunately most of the comparisons are meaningless since the wrong units are used. For amagnetic refrigerator, the engineer or designer needs to know the cooling per unit volume, and

4 According to the two commonly known databases—ISI Web of Knowledge, http://isi4.isiknowledge.com/portal.cgiand Chemical Abstracts, http://www.cas.org/—the number of research articles containing the word ‘magnetocaloric’in the title, the abstract or in the list of keywords more than doubled over each of the two five-year periods from 1995to 1999 and from 2000 to 2004 when compared with the average over all of the five-year periods from 1970 to 1994,i.e. 22 per five years before 1995, to 79 and 311, respectively, according to ISI Web of Knowledge. Even though thefigures extracted from the Chemical Abstracts are different, which is related to the differences in both the databasecontent and in the search-and-match algorithms, the trend is practically the same: from 54 on average per five-yearperiod between 1970 and 1995 to 135 and 438 over each of the last two five-year periods.


Figure 1. The total entropies in the initial (Hi) zero and final Hf ) magnetic fields (a), and theMCE (b) in the vicinity of the Curie temperature of gadolinium, a ferromagnet with zero coercivityand remanence plotted as functions of reduced temperature.

thus the only units which are meaningful for such comparisons are mJ cm−3 K−1, and for thisreason we have converted the reported �SM to volumetric entropy units in this review. Sincethe J kg−1K−1 units are easily converted to the mJ cm−3 K−1 values if the density is known andsince the density is not readily available (although it is easy to calculate if the crystal structureand lattice parameters are known), we have included the densities in the tables along with the�SM values, and after the compound if �SM is given in the text. This will enable the readerto quickly change the values given in this review to the J kg−1 K−1 of J mol−1 K−1 scales.

Furthermore, since in the vast majority of cases the magnetic entropy change is negativewhen the magnetic field increases but materials where the sign of the MCE is reversed arealso known, the sign of �SM will be properly reflected in all the tables and in the figures. Inthe text and in all the discussions when we compare the MCEs of several materials, we willcompare the magnitudes only. Hence, a 50% reduction of the �SM, for example, means thatits absolute value (and therefore the magnetothermal response) is reduced by 50%.

2. Theory

For a given material at a constant pressure, the two quantitative characteristics of the MCE arefunctions of the absolute temperature (T ) and the magnetic field change (�H = Hf − Hi),where Hf and Hi are the final and initial magnetic fields, respectively, experienced by thematerial. The MCE can be easily computed [14] provided the behaviour of the total entropy(S) of a compound is known as a function of temperature in constant magnetic fields Hf andHi, e.g. see figure 1(a) which depicts the total entropies and figure 1(b) which illustrates both�SM and �Tad of a ferromagnetic material in the vicinity of its Curie temperature:

�SM(T , �H)�H = S(T , H)T,H=Hf − S(T , H)T,H=Hi , (1)

�Tad(T , �H)�H = T (S, H)S,H=Hf − T (S, H)S,H=Hi . (2)


Direct isothermal measurements of the heat transfer and, therefore, direct measurementsof �SM using equation (1) are inconvenient and they are rarely, if ever, performed inpractice. However, equation (2), in which the dependent variable (entropy) and the independentvariable (temperature) are switched when compared with equation (1), can be and are oftenstraightforwardly employed in direct measurements of �Tad [15–17]. Thus, the temperatureof a sample is measured in both Hi and Hf , i.e. before and after the magnetic field has beenchanged. The difference between the two temperatures yields the intensive MCE value. Both�SM and �Tad are usually reported as functions of temperature when Hi = 0 and Hf > Hi.

At equilibrium, the MCE is correlated with the magnetization (M), magnetic field strength(H ), heat capacity at constant pressure (C) and absolute temperature by one of the followingfundamental Maxwell equations (where µ0 is the permeability of vacuum):

�SM(T , �H)�H = µ0

∫ Hf

Hi

(∂M(T , H)

∂T

)H

dH, (3)

�Tad(T , �H)�H = −µ0

∫ Hf

Hi

(T

C(T , H)× ∂M(T , H)

∂T

)H

dH. (4)

As immediately follows from equations (1)–(4), materials whose total entropy is stronglyinfluenced by a magnetic field and whose magnetization varies rapidly with temperatureare expected to exhibit an enhanced MCE. The latter peaks when |(∂M(T , H)/∂T )H | isthe greatest, i.e. around the TC in a conventional ferromagnet or near the absolute zerotemperature in a paramagnet. The MCE of a simple ferromagnet is usually gradually loweredboth below and above the TC, as is clearly seen in figure 1(b).

Equations (3) and (4) are easily derived from general thermodynamics (e.g. see [13]),yet both fail to describe the MCE in the vicinity of a truly discontinuous first-order phasetransition when either [∂M(T , H)/∂T ]H or [T/C(T , H)]H or both do not exist. This occursbecause, by definition, the partial first derivatives of the Gibbs free energy with respect tointensive thermodynamic variables, e.g. T , P or H , vary discontinuously at the first-orderphase transition. As a result, the bulk magnetization is expected to undergo a discontinuouschange at constant temperature; and the heat capacity is expected to be infinite during afirst-order phase transformation. Thus, in theory, [∂M(T , H)/∂T ]H and [T/C(T , H)]H donot exist at the temperature of the first-order transition. In reality, these changes occur overa few Kelvin wide temperature range, and both functions can be measured experimentally.Other factors, for example time-, rate of temperature or magnetic field change-, temperature-and magnetic history-dependence of the magnetization, may severely affect the accuracy ofnumerical integration using equations (3) and (4), and therefore, they must be applied withcaution. Equations (1) and (2), on the other hand, fully define the MCE regardless of thethermodynamic nature of the phase transformation that occurs, if any, in a material.

Equation (3) is commonly employed to evaluate the isothermal magnetic entropy change(e.g. see [18] and [19]) because bulk magnetization data as a function of temperature andmagnetic field are relatively easy to obtain. Equation (4), however, is seldom used for practicalcomputations since it is difficult to measure the magnetic field and temperature dependent heatcapacity with the resolution and accuracy required for a reliable numerical integration.

For a first-order phase transition, it is also possible to employ an approximation which isbased on the Clausius–Clapeyron equation:

−(

dH

dT

)eq

=(

�S

�M

)T

. (5)

In equation (5), the left-hand side derivative is taken under equilibrium conditions, i.e. whenthe Gibbs free energies of the two phases are identical to one another. For the right-hand


side, �S = Sf − Si and �M = Mf − Mi, where the subscripts i and f correspond to phasesin the initial magnetic field and in the final magnetic field states, respectively. Obviously,equation (5) is only applicable when Hf is strong enough to complete the transformation froma state i to a state f and when the quantity dH/dT at equilibrium is known. In other words,the H–T phase diagram for the system must be well established. Furthermore, by using theClausius–Clapeyron equation, an estimate of only the extensive MCE, �SM = �S, is possible.In order to find more about the thermodynamics of the MCE, we refer the interested reader toseveral recent reviews [6, 7, 20], and a monograph by Tishin and Spichkin [13]. A few updatesin the understanding of the MCE that occurred after these reviews were published are brieflymentioned in the following paragraphs.

Gschneidner et al [21] described successful use of the alloy theory, based on which theywere able to design novel materials exhibiting enhanced MCEs below 100 K. The major issuestaken into account by this work were the availability of the magnetic entropy (i.e. the theoreticalentropy change when a spin system switches from a complete disorder to a perfect magneticorder), the systematic variation of the magnetic properties of lanthanides as the number of4f-electrons changes and the ability to adjust the Curie temperature of a material by alloyingwith other lanthanides, as well as with the non-magnetic elements. Typical improvements overthe existing prototypes reported in [21] were of the order of 30%.

Pecharsky et al [14] give a detailed examination of the behaviour of the total entropy in thevicinities of both first- and second-order phase transitions. They conclude that in second-ordermagnetic phase transition (SOMT) systems, the largest MCE is expected when the heat capacityof a material is strongly influenced by the magnetic field. In the case of first-order magneticphase (FOMT) transformations, the maximum magnetic entropy change is principally definedby the difference in the entropies of the low- and high-magnetic field phases—the larger theentropy difference, the larger the corresponding �SM. The largest �Tad are predicted to occurin first-order materials whose Curie temperature is strongly affected by the magnetic field, inother words the greater dTC/dH corresponds to the greater �Tad.

By using Ginzburg–Landau theory to analyse available experimental data for Co(S,Se)2,Lu(Co,Al)2, Lu(Co,Ga)2, U(Co,Fe)Al, MnFe(P,As) and La(Fe,Si)13 compounds, Yamada andGoto [22, 23] show that in the case of itinerant electron metamagnetic (IEM) systems exhibitingthe GMCE, the temperature dependence of the critical magnetic field of the metamagnetictransition plays an important role in maximizing the isothermal magnetic entropy change.Furthermore, the GMCE in other IEM systems is expected to occur when the M4 pre-factor inthe Landau energy expansion with respect to magnetization is negative and large. The lattercoincides with conclusions arrived at by Amaral and Amaral [24] who applied Landau theory toferromagnetic systems with magnetoelastic and magnetoelectronic couplings. Similar resultswere also reported by von Ranke et al [25], who modelled the effects of both externally(magnetic field and pressure) and internally (deformation of the unit cell) controlled parameterson the MCE in systems with localized magnetic moments.

Lima et al [26] derived the anisotropic MCE in single crystals of some RAl2 and RNi2compounds, where R = lanthanides, considering a Hamiltonian which takes into accountcrystalline electric field (CEF) and quadrupolar effects in addition to magnetoelastic couplingand nearest neighbour interactions. In some cases, both the MCE and cooling capacity may beconsiderably increased if during the magnetizing–demagnetizing of a magnetocaloric materialthe orientation of the magnetic field vector is synchronized with the variable easy magnetizationdirection of such a crystal. An interesting claim has been made recently by Zhitomirsky [27],who finds that the MCE in strongly frustrated Heisenberg antiferromagnetic systems, such asthose containing triangular networks of atoms (e.g. kagome nets), is intrinsically higher thanin non-frustrated systems. The enhancement originates from a number of soft modes present


in frustrated systems below the saturation field. By using a Hamiltonian that takes into accountthe dipolar and quadrupolar interactions in addition to CEFs, de Oliveira et al [28] theoreticallyexamined the nature of a nearly flat, ‘table-like’ MCE of the doublet–triplet �3–�5 reducedmagnetic system. While it has been found experimentally (e.g. see [29]) that the table-likeMCE is the result of successive magnetic phase transformations, de Oliveira and co-workersestablished a suitable energy gap between �3–�5 that permits successive magnetic orderingsat different temperatures. It is worth noting that their theoretical predictions of the table-likeMCE in TmZn and TmCd await an experimental verification.

3. Elements and their solid solutions

Little research has been carried out on the pure magnetic elements and their solid solution alloysin the past four years. The status of the MCE in these materials will be found in [7, 12, 13].

Chernyshov et al [30] have studied the MCE of a single crystal of a high purity Dymetal when the magnetic field was applied in the easy magnetization direction (the a-axis)in fields up to 14 kOe. In general, their results were in good agreement with the prior resultson lower purity polycrystalline Dy. However, the authors discovered two new high-magneticfield phases in the 105 to 127 K and 179 to 182 K temperature regions, and a new magneticphase diagram was proposed. A fairly substantial positive MCE (i.e. �Tad > 0) is observedat ∼90 K at the first-order antiferromagnetic to ferromagnetic transition (on cooling) whichrises much more steeply and is about 10–30% larger than previously observed. Between 160and 180 K there is a small negative �Tad which is about the same as previously observed.However, between 180 and 210 K there is again a positive MCE which is about a factor of 2larger than previously observed in the lower-purity polycrystalline Dy.

The effect of doping a 50 : 50 Gd : Dy alloy with Nd (up to 30%) was studied by Daiet al [31], who found that the Curie temperature is lowered from 235 K for the parent alloyto 165 K for Gd0.35Dy0.35Nd0.30. The �SM was reduced by 15% at the respective orderingtemperature by the substitution of Nd for Gd : Dy. Upon storage in air for two years, themagnetization of the Nd containing alloys decreased by about 20%, while those with no Nddid not change. This will have a notable effect on the MCE properties of the Nd substitutedalloys.

The doping of Gd1−xTbx alloys with Nd up to 15% was studied by Zhang et al [32]. Theyfound that both Tb and Nd additions to Gd lower the Curie temperature of Gd and that smalladditions of Nd (∼5%) have only a slight influence on the MCE of the Gd1−xTbx alloy.

Wang et al [33] found that B additions to Gd (2, 5 and 7 at%) expanded the unit cellvolume, raised TC by 4 to 298 K, increased the refrigeration capacity, q, by 12% and had noeffect on �SM. The variation of the lattice parameters and TC with the B content suggestedthat the maximum solid solubility of B in Gd is 2 at% or less. However, the second phaseGdB2 seems to increase q by increasing the breadth of the caret-like shape of the �SM versusT peak.

The temperature dependence of the MCE of Er is quite complex, as one might expect, sinceit has a first-order magnetic transition at 18.7 K, two second-order transitions at 52.7 and 86.4 Kand a spin–slip transition at 26.2 K. The addition of Pr to Er (Er1−xPrx for 0 � x � 0.30) hasbeen studied by Wu et al [34]. They found that the 86.4 K ordering temperature is lowered andthat of the first-order peak at 18.7 K is raised by Pr additions. As a result, the �Tad at 18.7 K inpure Er is reduced by about one-third for x � 0.1 for a magnetic field change of 0 to 20 kOe,while the MCE of the upper transition (86.4 K) increases by a factor of 2. This results in anearly constant MCE between 35 and 50 K for 0.1 � x � 0.3. For a 0 to 50 kOe field change,the MCE associated with the 18.7 K transformation is also decreased for 0.1 � x � 0.2, but for


Magnetic field change, ∆H (kOe)

0 20 40 60 80 100

Mag

neto

calo

rice

ffect

,-∆

M(m

J/cm

3K

)

0

20

40

60

80

100

120

140

160

180

200

220

Gd5(Si2Ge2)

TC

= 270 K

GdTC

= 294 K

DyCo2TC

= 142 K

La(Fe11.375Al1.625)

TC

= 145 K

La(Fe11.44Si1.56)

TC = 195 K

MnAsTC

= 318 K

(La0.7Ca0.3)MnO3TC = 227 K

Magnetic field change, ∆H (kOe)

0 20 40 60 80 100M

agne

toca

loric

effe

ct,∆

(K)

0

5

10

15

20

GdGd5(Si2Ge2)

La(Fe11.44Si1.56)

DyCo2

MnAs

TC = 270 K

TC = 294 K

TC = 195 K

TC = 142 K

T C=

318

K

(a)

Mag

neto

calo

rice

ffect

,–∆S

M(m

J/cm

3)

Gd5(Si2Ge2)

TC

= 270 K

GdTC

= 294 K

DyCo2TC

= 142 K

La(Fe11.375Al1.625)

TC

= 145 K

La(Fe11.44Si1.56)

TC = 195 K

MnAsTC

= 318 K

(La0.7Ca0.3)MnO3TC = 227 K

Mag

neto

calo

ricef

fect

,∆T

ad

(K)

GdGd5(Si2Ge2)

La(Fe11.44Si1.56)

DyCo2

MnAs

TC

TC

TC = 195 K

TC

T C=

318

K

(a)

K

(b)

Figure 2. The isothermal entropy change as a function of the magnetic field change forDyCo2 [48–50], Gd5(Si2Ge2) [51], La(Fe11.44Si1.56) [52], La(Fe11.375Al1.625) [53], Gd [54],(La0.7Ca0.3)MnO3 [55] and MnAs [56]. The data points for DyCo2 at 4, 8 and 10 kOe weretaken from [48], the data points at 20, 50, 75 and 100 kOe from [49] and that at 70 kOe from [50].The highest values of −�SM for Gd5(Si2Ge2) and the two highest values for Gd are unpublishedresults of the authors (a). The adiabatic temperature rise as a function of the magnetic field changefor DyCo2 [49], Gd5(Si2Ge2) [51], La(Fe11.44Si1.56) [52], Gd [7] and MnAs [56]. The highestvalue of �Tad for Gd5(Si2Ge2) is an unpublished result of the authors (b).

x = 0.2 the upper ordering temperature has been lowered to ∼50 K and its MCE is increasedby ∼20% compared with the �Tad value for the 18.7 K peak of pure Er.

4. Binary and ternary intermetallic compounds

4.1. Laves phases

4.1.1. RCo2-based systems. The RCo2 phases have been extensively studied because three ofthem exhibit a first-order paramagnetic–ferromagnetic transition (R = Dy, Ho and Er) whilethe other RCo2 phases become ferromagnetic via a second-order transition. The work carriedout before 2000 is summarized in [7, 12]. Most of the recent studies involve the substitutionof a rare-earth metal for one of the magnetic lanthanides [35–39] or the substitution of a non-rare-earth metal for Co [36, 40–47]. But as a result of these studies most investigators alsomeasured �SM for the pure binary RCo2 phase and confirmed the earlier reported results. Oneexception was the study by Wang et al [48], who measured the variation of �SM at low fields (4,8 and 10 kOe); in all the earlier studies the lowest applied magnetic field was 10 kOe or higher.The variation of �SM versus the applied magnetic field for DyCo2 is shown in figure 2(a) and�Tad is shown in figure 2(b) along with several other materials which are discussed in latersections. It is seen that the �SM values for DyCo2 are fairly large and are grouped with othermaterials which have FOMT [Gd5(Si2Ge2), MnAs and La(Fe11.44Si1.56)], but �Tad is quitesmall and is close to that of La(Fe11.44Si1.56), but is significantly smaller than those for MnAsand the 4f-based materials [Gd and Gd5(Si2Ge2)]. It is noted that �SM values reported by [36]for �H = 20 kOe and 50 kOe for DyCo2 are ∼30% and ∼15% smaller, respectively, than


Table 1. The magnetocaloric properties of selected RM2 Laves phases.

−�SM (mJ cm−3 K−1) �Tad (K)Density

Compound TC (K) 0–20 kOe 0–50 kOe 0–20 kOe 0–50 kOe (g cm−3) Ref.

TbCo2 236 26 48 1.9 3.6 9.087 [49]DyCo2 142 101 128 4.5 6.3 10.013 [49]HoCo2 83 112 203 4.0 8.8 10.172 [49]ErCo2 37 300 331 3.0 7.4 10.343 [49]

the results given in figure 2(a). However, the values reported by the same authors for TbCo2

and HoCo2 are in much better agreement with the results reported by other investigators. TheMCE properties of some of the RCo2 phases for magnetic field changes of 0 to 20 kOe and 0to 50 kOe are shown in table 1. As expected, the RCo2 phases undergoing an FOMT exhibithysteresis, which is fairly small (2 kOe) for DyCo2 but increases with decreasing TC (5 kOe)for ErCo2. For more details and further discussion, see section 11.3.1 and table 8.

The effect of substituting one magnetic lanthanide, R′, for the original lanthanide, R,raises or lowers TC as one might expect from the respective de Gennes values of R and R′.The MCE of DyCo2 is rapidly lowered by Gd substitution [35] and that of TbCo2 is raised byEr substitutions [37]. de Oliveira et al [39] calculated the variation of TC, �SM and �Tad for(Er1−xDyx)Co2 alloys for 0.2 � x � 1.0 based on the measured values of ErCo2. Duc et al[36, 38] noted that when 35% of Y and Lu were substituted for Gd in GdCo2 there was littleeffect on �SM, and similarly for a (Gd0.4Tb0.6)Co2 alloy.

The influence of M substitutions (M = Al, Si, Ga, Ge) for Co in the DyCo2 compoundhas been extensively studied, especially for M = Si [41, 43–45], while only [42] and [44]studied M = Al, and [44] examined Ga and Ge substitutions. The behaviours of the fourM elements are similar: (1) TC is increased and Al is more effective than Ga, which is followedby Si and then Ge; (2) �SM drops off rapidly for x > 0.02 because the FOMT is destroyed byM substitutions and is changed to an SOMT; and (3) �SM reaches a value 70% of the �SM

value of pure DyCo2 (see table 1) when x = 0.1 for M = Al, Ga and Ge (the maximumsolubility of Si in DyCo2 is 7%, i.e. x = 0.07).

Troper et al [46] calculate the effect of Rh substitution for Co on the magnetic behaviourof HoCo2. The TC of HoCo2 (83 K) is rapidly lowered by initial Rh addition to ∼55 K at5 at% Rh, and then more slowly to HoRh2 (TC = 20 K). The FOMT of HoCo2 changes to anSOMT between 5 and 15 at% Rh. The �SM of HoCo2 for a field change of 50 kOe increasesby ∼12% for Ho(Co0.95Rh0.05)2 and drops by ∼40% at 15 at% Rh. The �Tad for the same�H is predicted to drop slightly for a 5 at% Rh substitution (∼7%) and then drop more rapidlyfor a 15 at% Rh substitution (∼35%).

When Si is substituted for Co in ErCo2 (0 � x � 0.15), TC raised from ∼35 to ∼60 Kwhile �SM is lowered 37% for x = 0.05 and 85% for x = 0.15 [36]. The rapid drop in�SM is due to the change of the FOMT in ErCo2 to SOMT when some of the Co is replacedby Si, i.e. when x > 0.02. Similar results were reported by Singh et al [47]. When Niis substituted for Co in ErCo2, TC is lowered to ∼12 K at x = 0.10, while �SM and �Tad

remain about the same for x = 0.05, but then decrease by ∼20% and ∼30%, respectively, forx = 0.10.

Duc et al [36] noted that �SM decreases with increasing temperature for the R(Co1−xSix)2

compounds, where R = Er and Ho, and the (Dy1−xYx)Co2 phases which exhibit FOMT, andthat it lies well above the �SM values for the RAl2-based compounds and Er(Co1−xSix)2 forx = 0.10 and 0.15 phases which exhibit SOMT. A modified version of this plot is shown in


∆

T

Figure 3. The magnetic entropy change for �H = 50 kOe for the RCo2, RAl2, Gd5(Si1−xGex)4,Mn(As1−xSbx ), MnFe(P1−xAsx ) and La(Fe13−xSix ) families plus a number of individualcompounds versus the Curie temperature. The original plots for the RCo2 and RAl2 familiesgiven in [36] had many more data points, but only selected values were used here, primarilybecause density or lattice parameters were not available for most of the ternary compounds andthus the entropy units used in [36] could not be converted to the volumetric units used in thisfigure. The solid lines tie together those members of a family which exhibit a FOMT, while thedashed line and dotted line tie together those compounds of a family which have a SOMT. Forthe Gd5(Si1−xGdx)4 family the solid squares are for those compounds which exhibit FMOTO(I)–O(II) transition, the solid triangles represent those for the FOMT O(I)–M transition, whilethe solid dots are for the SOMT O(I) ferromagnetic-paramagnetic transition (see section 5 formore details). The value for Gd was taken from [54]. The values in square brackets after thecompounds in the legend identifying the compounds are the densities in g cm−3 units.

Compound legend1—ErAl2 [6.204] 16—DyCo2 [10.013] 31—Gd5Si2.1Ge1.9 [7.493]2—(Dy0.7Er0.3)Al2 [6.048] 17—Gd [7.901] 32—HoCoAl [7.961]3—DyAl2 [5.981] 18—Gd5Si2.3Ge1.7 [7.472] 33—DyCoAl [7.619]4—TbAl2 [5.817] 19—Gd5Si3Ge [7.279] 34—TbCoAl [7.649]5—(Tb0.4Gd0.6)Al2 [5.719] 20—Gd5Si4 [6.987] 35—GdCoAl [7.575]6—GdAl2 [5.690] 21—Gd5Si0.5Ge3.5 [7.909] 36—MnAs [6.799]7—Er(Co0.85Si0.15)2 [9.937] 22—Gd5SiGe3 [7.777] 37—MnFeP0.45As0.55 [7.256]8—TbCo2 [9.087] 23—Gd5Si1.2Ge2.8 [7.722] 38—TbN [9.567]9—Gd4Bi3 [10.073] 24—Gd5Si1.3Ge2.7 [7.700] 39—HoN [10.26]

10—Gd4(Bi2.25Sb0.75) [9.679] 25—Gd5Si1.5Ge2.5 [7.663] 40—Tb5Si2Ge2 [7.670]11—Gd4(Bi1.5Sb1.5) [9.679] 26—Gd5Si1.6Ge2.4 [7.647] 41—Dy5Si3Ge [7.739]12—Gd4(Bi0.75Sb2.25) [8.834] 27—Gd5Si1.8Ge2.2 [7.575] 42—La(Fe11.7Si1.3) [7.300]13—Gd4Sb3 [8.414] 28—Gd5Si1.95Ge2.05 [7.530] 43—La(Fe11.5Si1.5)H1.8 [7.003]14—ErCo2 [10.343] 29—Gd5Si1.98Ge2.02 [7.525] 44—La1.4Ca1.6Mn2O7 [5.536]15—HoCo2 [10.172] 30—Gd5Si2.02Ge1.98 [7.517] 45—Gd5Sn4 [8.727]

46—Ni55.2Mn18.6Ga26.2 [8.247]

figure 3, where the �SM values for the FOMT RCo2-based phases (points 14–16) lie abovethose for the SOMT RCo2-based and RAl2-phase compounds. Also shown are the �SM valuesfor several families of compounds, some of which have both FOMT and SOMT. The �SM

values for the FOMT R5(Si1−xGex)4 compounds lie well above those for the FOMT RCo2

materials. However, the �SM values for the SOMT phases of these families are comparablewith those of the SOMT RCo2 intermetallics (points 7 and 8 in figure 3). The similarities in the


behaviours (i.e. the large difference in FOMT and SOMT �SM values) of the Gd5(Si1−xGex)4

intermetallics and the RCo2-based compounds is evident.Theoretical modelling of the MCE in (Er1−xYx)Co2 for x = 0 and 0.2 [57] and for

Er(Co1−xNix)2 [58] has been carried out using a mean-field approach and treating the disorderin the coherent-potential approach, also see section 2. The calculated �SM and �Tad valuesare in good agreement with earlier published experimental data.

4.1.2. RAl2-based systems. Only seven papers have been published on the RAl2 phasessince 1999, four experimental and three theoretical. The MCE of GdAl2 [58, 59], TbAl2 [60],(Gd0.6Tb0.4)Al2 [60] and a series of (Tb1−xYx)Al2 alloys [61] have been measured, whiletheoretical calculations of the MCE of RAl2 (R = Pr, Nd, Tb, Dy, Ho, Er and Tm) [62], DyAl2[63] and the (Dy1−xErx)Al2 pseudo-binary system [64] were reported.

The experimental data reported for GdAl2, TbAl2 and (Gd0.6Tb0.6)Al2 are consistent withthe other RAl2 values, see figure 3, points 1–6. For (Tb1−xYx)Al2 (density for x = 0.5 is4.866 g cm−3), Bohigas et al [61] found spin glass behaviour for 0.50 � x � 0.85, with theordering temperatures falling from 30 K at x = 0.50 to 10 K at x = 0.85, and the MCE alsodecreased rapidly with increasing x, by 85% over the same concentration range. The authorsreported �SM = −37 mJ cm−3 K−1 for a 0 to 20 kOe magnetic field change for x = 0.50(TC = 30 K). We estimate �SM to be about −90 mJ cm−3 K−1 for �H = 50 kOe, which issignificantly smaller than the expected value for TC = 30 K for the RAl2 phases (see figure 3).But this value is not unreasonable since the concentration of the magnetic metal (Tb), whichaccounts for the MCE, is 50% of that found in undiluted RAl2 phases which established theSOMT curve shown in figure 3.

The Brazilian group [62–64] have carried out theoretical calculations for many of theRAl2 compounds using a Hamiltonian which included the CEF and exchange interactions.von Ranke et al calculated �SM for the RAl2 phases where R = Pr, Nd, Tb, Dy, Ho, Er andTm. The theoretical values for ErAl2 were in fair agreement with experimental results and ingood agreement for DyAl2. The experimental MCE values for the other RAl2 were not knownat that time, but they predicted that the maximum �SM value would be for ErAl2 and decreasein the order Ho to Dy to Tb for the heavy lanthanides with atomic numbers (Z) less than thatof Er. The �SM value for TmAl2 (where Z is one larger than that of Er) is less than that ofthe ErAl2 value but larger than that of HoAl2. For the light lanthanides PrAl2 and NdAl2, theMCE values are less than that of the heavy lanthanide with the same TC values.

In an earlier paper these authors [63] predicted a negative MCE when the magnetic fieldwas applied along the 〈111〉 direction in DyAl2 because there is an FOMT in the magnetizationin this direction at a critical field of 58 kOe. They also predicted that the MCE would be normalin the 〈100〉 and 〈110〉 directions. They [64] were also able to explain the anomalous peakobserved in the MCE at ∼10 K for the (Dy1−xErx)Al2 alloys for x = 0.3 and 0.5. In addition,the calculated �Tad values were in good agreement with experiment for all the measuredcompositions between DyAl2 and ErAl2.

4.1.3. RNi2-based systems. Two theoretical studies on the RNi2 phases have been carriedout on the RNi2 phases with R = Pr, Nd, Gd, Tb, Dy, Ho and Er. von Ranke et al [65], usinga model Hamiltonian that included anisotropic CEF and exchange interactions, predicted theMCE properties of the RNi2 phases for R = Pr, Nd, Gd, Tb, Ho and Er. For the ErNi2phase, the theoretical values for �SM were in excellent agreement with experiment and infair agreement for �Tad. The other RNi2 phases have not been studied experimentally. Themaximum �SM is predicted to occur for HoNi2, followed by Tb, Er, Gd, Nd and Pr. These MCE


values are comparable with those calculated by the same authors [62] for the correspondingRAl2 compounds. The �Tad values are also a maximum at HoNi2, but the order is somewhatdifferent from that for the �SM values, i.e. the �Tad value is second highest for ErNi2, followedby Dy, Tb, Nd, Gd and Pr [65]. The authors also predicted a second peak in the MCE values at∼1.5 K for HoNi2 which they thought was due to a high density of states at low temperatures.

In a more recent paper, von Ranke et al [66] examined the MCE in RNi2 for R = Nd, Gd,Tb, Dy, Ho and Er as potential magnetic refrigerants for an Ericsson cycle. They proposeda composite material consisting of ErNi2–DyNi2–TbNi2 as a refrigerant for the 7 K to 22 Ktemperature range.

4.2. Miscellaneous intermetallic compounds

A number of other intermetallic compounds have been studied for their MCE properties, bothbinary and ternary, and the reported results are divided into these two categories. In generalthe compounds are listed in order of increasing atomic number of the non-rare-earth metal (orelement). There are, however, several important families of intermetallic compounds which arebeing treated separately—the R5(Si,Ge)4 phases, the Mn-based materials and the La(Fe,M)13

compounds—sections 5, 6 and 7, respectively.

4.2.1. Binary compounds. Nakagawa et al [67] measured �SM and TC for seven compositionsin the (Gd1−xDyx)N system. TC was lowered in a nearly linear fashion from 61 K for GdNto 21 K for DyN. The MCE for a 0 to 10 kOe field change, however, was a maximum atDyN and decreased in a nearly linear fashion by ∼40% for (Gd0.9Dy0.1)N, but it jumped to asignificantly higher value at GdN (only ∼10% smaller than that of DyN). They also reportedthat �SM = −167 mJ cm−3 K−1 for �H = 50 kOe for DyN (density is 9.933 g cm−3). Thisvalue is comparable with those of the RAl2 phases at the corresponding TC, see figure 3.

The MCE properties of TbN and HoN were measured by Yamamoto et al [68]. Theyreported that �SM = −196 mJ cm−3 K−1 for a 0 to 50 kOe field change for TbN, TC = 44 K;and �SM = −291 mJ cm−3 K−1 for the same �H for HoN, TC = 18 K. Both these valueslie well above the SOMT line established by the RAl2 phases (figure 3), points 38 and 39,respectively, but below the RCo2 FOMT line.

The Gd-rich alloys in the (Gd1−xTbx)3Al2 system x = 0, 0.1, 0.2 and 0.3 were studiedby Long et al [69]. They found that Tb additions lower TC from 280 K for Gd3Al2 to 255 Kfor x = 0.3 and increase the �SM values for �H = 10 kOe from −14.9 mJ cm−3 K−1 forx = 0 to −18.0 mJ cm−3 K−1 at x = 0.1, and with further Tb addition �SM falls slightly to−17.4 mJ cm−3 K−1 at x = 0.3. The �SM values are about 75% of that of Gd metal, whichsuggests that for �H = 50 kOe these alloys would be close to the SOMT line of figure 3.

The antiferromagnetically ordered Nd compounds NdP (TN = 11 K) and NdAs (TN =12 K) were studied both theoretically and experimentally by Plaza et al [70]. The theoretical�SM value was calculated using a Hamiltonian that included CEF interactions and molecularand quadrupolar fields. The agreement with experiment was quite good on the high temperatureside of the caret-like shape of the MCE peak, but ∼10 K above TN, the theoretical valuesbecame significantly higher than the observed �SM curve. The experimental �SM valuesat TC were −52.6 mJ cm−3 K−1 for �H = 50 kOe for NdP (density is 6.149 g cm−3) and−70.2 mJ cm−3 K−1 for �H = 70 kOe for NdAs (density is 7.840 g cm−3). As expectedfor antiferromagnets, the �SM values are significantly smaller than those of ferromagneticsubstances.

The MCE properties of Nd2Fe17 (TC = 325 K) were determined by Dan’kov et al [59],see table 2: the �SM was slightly smaller than those of the Si-rich Gd5(Si1−xGex)4 alloys(figure 3) and �Tad was significantly smaller (see figure 4).


Figure 4. The adiabatic temperature change for the Gd5(Si1−xGex)4 and La(Fe13−xSix)Hy

families, and other selected compounds. The values for ErAl2 (point number 31) are unpublishedresults obtained by the authors.

Compound legend1—Gd5.00Si4.00 12—Gd5Si0.90Ge3.10 23—HoCo2

2—Gd5Si3.50Ge0.50 13—Gd 24—DyCo2

3—Gd5Si3.00Ge1.00 14—La(Fe11.70Si1.30) 25—TbCo2

4—Gd5Si2.50Ge1.50 15—La(Fe11.57Si1.43) 26—Gd4Bi35—Gd5Si2.09Ge1.91 16—La(Fe11.44Si1.56) 27—Gd4(Bi2.25Sb0.75)

6—Gd5Si2.00Ge2.00 17—La(Fe11.44Si1.56)H0.5 28—Gd4(Bi1.5Sb1.5)

7—Gd5Si1.98Ge2.02 18—La(Fe11.44Si1.56)H1.0 29—Gd4(Bi0.75Sb2.25)

8—Gd5Si1.80Ge2.20 19—La(Fe11.70Si1.30)H1.1 30—Gd4Sb3

9—Gd5Si1.72Ge2.28 20—La(Fe11.57Si1.43)H1.3 31—ErAl210—Gd5Si1.50Ge2.50 21—La(Fe11.44Si1.56)H1.5 32—MnAs11—Gd5Si1.00Ge3.00 22—ErCo2

The �Tad value of 5 K for Gd3Co at TC = 135 K for �H = 40 kOe [71] is rather modestcompared with other materials which have comparable TCs, see figure 4.

The MCE in TmCu and TmAg, which have the simple CsCl-type structure, was studiedextensively by Rawat and Das [72]. Tm has both a large magnetic moment and a 4f-electronic-quadrupole in these two compounds and this leads to interesting magnetic behaviours at lowtemperatures. TmCu orders antiferromagnetically with an incommensurate antiferromagneticstructure at 7.7 K, which transforms to a commensurate structure at 6.7 K. Both transformationsare first order. In TmAg, there is only one second-order paramagnetic to antiferromagnetictransition at 9.5 K. The antiferromagnetic nature of the ground states of TmCu and TmAgleads to a negative MCE at low temperatures less than 8 K and 10 K, respectively, and a normalMCE above these two temperatures, see table 2. The corresponding absolute MCE peak valuesare much larger for TmCu than for TmAg, but even the normal MCE values for TmCu aresignificantly smaller than that observed in other materials which order magnetically below10 K, such as ErNiAl and ErNi2 [12].

Aoki et al [73] studied the low temperature magnetothermal properties of single crystallineHoGa2, which has the hexagonal AlB2-type structure, and initially orders antiferromagnetically


Table 2. The magnetocaloric properties of selected binary intermetallic compounds.



Nd2Fe17 325 25 46 1.9 4.0 7.797 [59]Gd7Pd3 323 22 57 3.0 8.5 8.707 [75]Gd4Bi3 332 15 27 2.2 4.2 10.073 [77]Gd4(Bi2.25Sb0.75) 308 27 47 3.7 6.8 9.679 [77]Gd4(Bi1.5Sb1.5) 289 24 47 3.1 6.5 9.259 [77]Gd4(Bi0.75Sb2.25) 273 26 49 3.2 6.4 8.834 [77]Gd4Sb3 265 29 55 3.2 6.4 8.414 [77]Gd2In 194 18.5 37 2.0 4.4 8.316 [76]Gd2In ∼50a −12 −4 −0.7 −0.2 8.316 [76]TmAg ∼12b 11 74c 0.8 4.2c 10.169 [72]TmAg ∼7a −26 −55c −0.4 −0.9c 10.169 [72]TmCu ∼10b 25 118c 0.6 3.6c 9.692 [72]TmCu 6.7d −68 −131c −0.4 −1.8c 9.692 [72]

a Temperature at which �SM has the largest positive value and �Tad has the largest negative MCEvalue.b Maximum in MCE (no magnetic ordering observed at this temperature).c Interpolated.d Neel temperature.

below 8.5 K. HoGa2 has a complicated magnetic phase diagram and thus exhibits unusualMCEs as a function of temperature and applied magnetic field. Both positive and negative�Tad values have been observed, while �SM tends to be primarily positive. Both �Tad and�SM are fairly small.

The MCE in YbAs has been studied theoretically by von Ranke et al [74] because it is aheavy fermion compound in which there is a competition between magnetic interaction andKondo hybridization. The authors calculated that YbAs, which orders antiferromagneticallyat 0.49 K and H = 0, will exhibit a negative MCE between 33 and 84 K when �H is lessthan 23.5 kOe, and for field changes greater than this critical field the MCE is predicted to benormal.

Gd7Pd3, which orders at 323 K, has MCE values (see table 2) [75] comparable with thoseof Gd5Si3Ge (see figures 3 and 4), which has a similar Curie temperature.

Ilyn et al [76] studied the magnetothermal properties of Gd2In which ordersferromagnetically at 194 K and antiferromagnetically at 91 K. At 194 K, normal MCE valueswere measured (see table 2), with �SM values being slightly smaller than those of the RAl2Laves phases (figure 3) and �Tad values about half of those of the RAl2 compounds. Butbelow ∼100 K negative MCE values are observed for small �H , i.e. <50 kOe. The maximumanomalous MCE values of �SM and �Tad occur at ∼50 K for �H = 20 kOe and the absolutevalues are small, see table 2.

A series of alloys of the Gd4(BixSb1−x)3 system, which have the cubic anti-Th3P4 typestructure, were examined by Niu et al [77] and Niu [78]. All alloys order ferromagneticallyfrom 332 K for Gd4Bi3 to 265 K for Gd4Sb3. The MCE values for Gd4Bi3 (table 2)are significantly smaller than those of Gd5(Si3Ge) phase which orders at about the sametemperature. But the MCE values for Gd4(BixSb1−x)3 for 0 � x � 0.75 (table 2) aresignificantly larger than for the pure Gd4Bi3 phase and are in line with the trends establishedin figures 3 (points 9–13) and 4 (points 26–30).

The magnetic phase diagram of PrPb3, like HoGa2 (see above), is also complicated [79].PrPb3 exhibits an antiferroquadrupolar transition at 0.39 K and H = 0, which increases to


0.66 K at 60 kOe. It also forms a new magnetic phase at H > 15 kOe. As a result, �Tad hasall positive values at 0.23 K for all field changes up to 60 kOe, and both positive and negativevalues at 0.5 K as a function of the applied field.

4.2.2. Ternary and quaternary compounds. The ternary intermetallic compounds reviewedin this section are discussed in the sequence aluminides, silicides, germanides and stannides,and within each group by the simplest to the more complex chemical formula. The ternaryR5(Si1−xGex)4 compounds, however, are discussed in section 5, along with the R5(M, Sn)4

stannides, while ternary silicides and germanides containing Mn are reviewed in section 6 andthe La(Fe13−xMx) phases in section 7. The one quaternary compound, HoNi2B2C, is the lastcompound to be discussed in this subsection.

Si et al [80] measured the MCE properties (�SM) of amorphous NdFeAl (the densitywas assumed to be the same as for the crystalline form, i.e. 6.56 g cm−3), which has a Curietemperature of 110 K. The maximum �SM of −37 mJ cm−3 K−1 for �H = 50 kOe is quite lowcompared with most crystalline compounds (see figure 3) and is about typical for amorphousmaterials [7].

The crystalline RCoAl compounds, where R = Gd, Tb, Dy and Er, were studied byZhang et al [81] and have MCE values which are similar to those of alloys which exhibit asecond-order magnetic transition (i.e. the SOMT line in figure 3). The TC and �SM values arelisted in table 3 and shown in figure 3 (points 32–35). The complex Nd7Co6Al7 (density is6.487 g cm−3) alloy has small MCE values (�SM = −30 mJ cm−3 K−1 and �Tad = 2.7 K fora 0–50 kOe field change) at TC = 15.5 K [82].

Most of the rare-earth ternary silicides have low MCE values [83–87] with the exceptionof GdPd2Si and possibly GdFeSi. The only reported MCE values for GdFeSi (TC = 118 K)were for a 0–90 kOe field change [83]. Prorating the MCE values for a 0–50 kOe field changesuggests that the �SM value would lie above the dashed curve in figure 3, but �Tad wouldbe significantly lower than the values shown in figure 4 near 120 K. GdPd2Si, which has twoordering temperatures, 13 and 17 K, undergoes a metamagnetic transition at 10 kOe [84]. Themaximum �SM values (table 3) lie well below the SOMT line curve of figure 3, but the �Tad

(table 3) is quite large, comparable with the materials shown in figure 4. Das and Rawat[85] reported �Tad values for PrCo2Si2 and (Pr0.8La0.2)Co2Si2. Both compounds exhibitcomplex behaviours of the MCE. The former orders at 10, 17 and 31 K, and �Tad is negativeat all temperatures between 4 and 40 K with peaks (less negative �Tad values) at the orderingtemperatures for both �H = 20 kOe and �H = 80 kOe, the peaks being more pronouncedfor �H = 80 kOe, while (Pr0.8La0.2)Co2Si2 orders at 9 and 26 K and �Tad is positive below9 K and just barely negative from 9 to 80 K for �H = 20 kOe, and for �H = 80 kOe �Tad

is positive below 11 K and above 26 K and negative between 11 and 26 K [85]. The MCEof polycrystalline Gd2PdSi3 [86] and single crystal Tb2PdSi3 [87] have been reported. Aswith many of the ternary compounds, the MCE (both �SM and �Tad) behaviour for the twocompounds is quite complex—exhibiting both positive and negative values. Gd2PdSi3 is anantiferromagnet (TN = 21 K) in low-magnetic fields, but becomes ferro- (or ferri-) magnetic forH > 5 kOe. Tb2PdSi3 (TN = 23 K) orders ferromagnetically along the [1010] direction. Thecrystal structures of these two compounds are unknown, and so it is not possible to calculate the�SM values in mJ cm−3 K−1 units; however, a reasonable estimate of the density (∼8 g cm−3)suggests that the �SM values lie well below the SOMT line drawn in figure 3. The �Tad valuesfor Gd2PdSi3 also seem to be somewhat low compared with the materials shown in figure 4.

The MCE (�SM) has been measured for three RTiGe phases, R = Dy, Ho and Tm [88].The three compounds order antiferromagnetically at 180 K, 92 K and 15 K, respectively. Forthe 0–20 kOe and 0–50 kOe field changes, the Dy and Ho compounds exhibit a negative MCE


Table 3. The magnetocaloric properties of selected ternary intermetallic compounds.


Compound TCa (K) 0–20 kOe 0–50 kOe 0–20 kOe 0–50 kOe (g cm−3) Ref.

GdCoAl 100 37 79 — — 7.575 [81]TbCoAl 70 41 80 — — 7.649 [81]DyCoAl 37 70 125 — — 7.619 [81]GdRu2Ge2 34 23 56b 1.5 4.0c 9.459 [91]GdPd2Si 17 42 142 3.2 8.6 9.358 [84]HoCoAl 10 100 171 — — 7.961 [81]

a Curie temperature, or temperature at the maximum (or minimum) MCE value.b Estimated from values obtained for magnetic field changes of 20 and 40 kOe.c Interpolated from values obtained for magnetic field changes of 40 and 60 kOe.

below TN but change to small positive MCE at TN due to a field induced antiferromagneticto ferromagnetic transition. The corresponding �SM values for TmTiGe are positive, whichmeans that fields >20 kOe are sufficient to suppress the antiferromagnetic state. For a 0–50 kOefield change the MCE at TN is �SM = −14 mJ cm−3 K−1 for DyTiGe (density is 7.571 g cm−3),−49 mJ cm−3 K−1 for HoTiGe (density is 7.698 g cm−3) and −75 mJ cm−3 K−1 for TmTiGe(density is 8.024 g cm−3), all of which are significantly smaller than the values which were usedto establish the SOMT curve in figure 3. The �Tad values have been reported for CeCu0.86Ge2

and PrCu0.76Ge2 by Rawat and Das [89]. The former orders at 17 K and has �Tad = 3.2 K for�H = 50 kOe, while the latter orders at ∼23 K and its �Tad = 4.0 K for �H = 50 kOe. Theauthors did not report �H = 50 kOe data, but we have estimated �Tad by interpolation usingthe 0 to 40 and 0 to 80 kOe curves. As seen, these �Tad values are quite a bit lower than thevalues of other materials shown in figure 4 for the corresponding ordering temperature. TheMCE (both �SM and �Tad) of GdRu2Ge2 was determined by Tegus et al [90], see table 3.GdRu2Ge2 undergoes two magnetic transitions at 29 and 32 K, but only one MCE peak isobserved at 34 K. The MCE is quite small: the |�SM| value lies well below the SOMT lineshown in figure 3, and the �Tad values also lie well below the data points in figure 4.

The MCE (both �SM and �Tad) of Er6Ni2Sn (density is 9.613 g cm−3) was measured formagnetic field changes of 0 to 10, 25, 30 and 80 kOe [91]. This compound orders at 7, 17 and35 K, and the maximum MCE values were observed at 17 K. By interpolation, the estimated�SM values for �H = 20 kOe and 50 kOe are −24 mJ cm−3 k−1 and −91 mJ cm−3 K−1,respectively. The latter value falls well below the SOMT curve in figure 3. The corresponding�Tad values are 0.8 K and 2.7 K, respectively, which also are quite low compared with thevalues plotted in figure 4 near T = 20 K.

The MCE properties of single crystal HoNi2B2C (density is 8.063 g cm−3), which ordersantiferromagnetically at 4.5 K, were measured by El Massalami et al [92]. Negative MCEvalues (for H parallel to a) were observed for field changes up to 10 kOe at ∼5 K for �SM

and at ∼20 K for �Tad. For field changes �20 kOe positive MCE values were measured: fora 0–50 kOe field change �SM = −128 mJ cm−3 K−1 and �Tad = 12 K at ∼8 K. These valueswere obtained by interpolation of the reported �H = 40 kOe and �H = 60 kOe results.

5. Gd5(Si1−xGex)4 and related 5 : 4 materials

5.1. General comments

Since the discovery of the GMCE in Gd5Si2Ge2 in 1997 [10], about 140 papers havebeen published by mid-2004 on the R5T4 materials, where R = a rare-earth element and


Figure 5. The magnetic phase diagram of the Gd5Si4–Ge5Ge4 pseudo-binary system. Thethin solid lines indicate magnetic phase boundaries, and the vertical dotted lines delineate theregions where the alloys are single phase materials (the compositions within shaded areas are two-phase alloys). The circles (open [heat treated] and solid [as cast]) refer to magnetic transitiontemperatures of the monoclinic Gd5Si2Ge2-type phase, the solid squares indicate the magnetictransition temperatures of the orthorhombic Gd5Si4-based phase, and the solid triangles anddiamonds refer to the magnetic transition temperatures of the orthorhombic Gd5Ge4-based phase,respectively, [98]. PM—paramagnetic, FM—ferromagnetic and AFM—antiferromagnetic.

T = Si, Ge or Sn. The interest in these phases and the excitement is not only due to theGMCE, but can also be ascribed to a number of other unusual features observed in thesecompounds, such as a colossal magnetostriction and giant magnetoresistance (see [93] andreferences cited therein). These extremum behaviours are due to a coupled magnetic–structuralfirst-order transition in which slabs of a well defined arrangement of R and T atoms shift∼0.5 Å with respect to one another along the a-axis when the material transforms under theinfluence of temperature, magnetic field or pressure [94–96]. This shift gives rise to an ∼1%volume change at the FOMT. The phenomenon, which gives rise to the GMCE and otherextremum behaviours, is the transformation on cooling or the application of a magnetic fieldfrom either the paramagnetic (P) monoclinic Gd5(Si2Ge2)-type structure to the ferromagneticorthorhombic Gd5Si4-type structure, or the antiferromagnetic (AFM) Sm5Ge4-type structureto the ferromagnetic (FM) orthorhombic Gd5Si4-type structure. The interesting features ofthese transformations are that T–T bonds between the slabs are absent in the Sm5Ge4-typestructure, or that they are absent between alternate slabs (i.e. two slabs have paired T–T atomsbetween them, but there are no T–T atom bonds between the paired slabs and the neighbouringslabs) in the Gd5(Si2Ge2)-type structure, but that the T–T atoms are present between all theslabs in the Gd5Si4-type structure [93, 95]. Another interesting feature is that the FOMTtemperature in the Gd5(Si1−xGex)4 is strongly dependent on the Si : Ge ratio, especially forx � 0.5 [97], see figure 5.

The MCE values reported by various researchers can vary considerably, but this canbe ascribed to the complex structural–metallurgical behaviour of many of these materials


especially for the Gd5(Si1−xGex)4 phases forx ∼= 0.5 [51, 98–100]. Also interstitial impurities,especially C, can have a pronounced effect on the MCE behaviour [101–103]. Unfortunatelymany researchers do not realize that most commercially available rare-earth metals have a largecontent of interstitial impurities, primarily H, C, N and O. When considered on an atomic basis,the interstitial content varies from 2 to 5 at%, that is, the purity of the starting rare-earth metalsis 98–95 at% (see [104] and references cited therein). Thus, unless the interstitial content istaken into account the desired composition of the alloy is incorrect. In addition, the alloy willcontain a substantial amount of C, N and O, and generally the H is lost in the preparationprocess due to its high vapour pressure. It is noted that most vendors claim their rare-earthmetals are 99.9% pure; this, however, is in reference to the other rare-earth elements only.

5.2. Gd5(Si1−xGex)4 alloys

The MCE in Gd5(Si1−xGex)4 alloys has been reported by a number of investigators[10, 51, 97–101, 103, 105–109]. The original report [10] of the GMCE in Gd5(Si2Ge2) showeda large narrow FOMT heat capacity peak at 276 K and a small lambda-type SOMT heatcapacity peak at 299 K. The original interpretation of these data was that there was a PM toAFM transformation at 299 K and a first-order AFM to FM transformation at 276 K. However,later research showed that this sample actually consisted of two polymorphic phases of theGd5(Si2Ge2) composition, and that by proper heat treatment one could obtain either polymorphfree from the other phase [51, 98–100]. By proper heat treatment, the originally reported �SM

value for the GMCE [10] was increased by 80% and �Tad was increased by 55% [51]. The�SM values reported by the Ames Laboratory group [51, 98–100] using high purity (99.89 at%)Gd for the Gd5(Si1−xGex)4 alloys for a 0 to 50 kOe field change are plotted in figure 3 (points18–31) as a function of the magnetic ordering temperature, while the corresponding �Tad

values for 0–20 and 0–50 kOe field changes are plotted in figure 4 (points 1–12), also as afunction of the magnetic ordering temperature. The field dependence of �SM and �Tad ofGd5(Si2Ge2) is shown in figures 2(a) and (b), respectively, along with several other potentialmagnetic refrigerants including Gd metal. It is seen that the field dependence of the GMCEcompares quite favourably with the other substances, especially �Tad.

The observed MCE behaviours can be correlated with the phase relationships in theGd5Si4–Gd5Ge4 pseudo-binary system. As shown in figure 5 there are two terminal solidsolutions and one intermediate solid solution region in this system. The Si-rich terminalsolid solution has the Gd5Si4-type crystal structure from the melting point to 0 K and itundergoes a PM to FM SOMT upon cooling. It is interesting to note all these alloys haveTCs which are greater than that of pure Gd (TC = 293 K). The MCE for the Si-rich alloys, i.e.x � 0.56 is better than those of materials which order magnetically above 300 K and undergoan SOMT (see figures 3 [�SM] and 4 [�Tad]), but are smaller than those which exhibit anFOMT (see figures 3 and 4). In the intermediate solid solution region (0.42 � x � 0.52), thealloys undergo a coupled structural/magnetic FOMT from the PM monoclinic Gd5(Si2Ge2)-type structure to the FM Gd5Si4-type orthorhombic structure upon cooling. In the Ge-richside of this pseudo-binary system (x � 0.32) things are a little more complicated. The roomtemperature form has the Sm5Ge4-type orthorhombic structure which transforms magneticallyfrom a PM state to an AFM state upon cooling as shown in figure 5. Upon further cooling, theAFM state undergoes a coupled structural/magnetic FOMT to the FM modification which hasthe Gd5Si4-type orthorhombic structure. It is quite obvious that the Gd5(Si1−xGex)4 alloyshave significantly higher �SM values (see figure 3, solid squares [points 21–24] and solidtriangles [points 25–31]) than any other material which orders below ∼300 K. This is dueto the unique combination of a coupled first-order magnetic–structural transformation. This


is especially evident when the Gd5(Si1−xGex)4 values are compared with those of the RCo2

phases (points 14–16), which exhibit an FOMT, but there is no structure change associated withthe magnetic transformation, only a phase volume discontinuity. A similar trend is observedfor �Tad (figure 4) but it is not quite as distinct as seen in �SM.

Other MCE measurements on the Gd5(Si1−xGex)4 alloys have been reported by Teguset al [88], Thuy et al [105], Thuy [106] and Zhuo et al [107]. Tegus et al [88] found that �SM

(−252 mJ cm−3 K−1) for polycrystalline Gd5(Si1.65Ge2.35), which orders at 222 K, was signifi-cantly smaller when compared with other reported values for alloys near this composition, andthey thought it might be due to the quality of their sample or the presence of impurities. Theyalso studied single crystal Gd5(Si1.7Ge2.3), TC = 241 K and found that there was a measurableanisotropy of the MCE: �SM (all in mJ cm−3 K−1) = −335 when H was parallel to the a-axis,−350 when parallel to b, and −297 when parallel to c. The average, −327 mJ cm−3 K−1, fallsclose to the solid curve for the Gd5(Si1−xGex)4 series in figure 3. Thuy et al [105] andThuy [106] reported a �SM value of −150 mJ cm−3 K−1 for Gd5(Si2Ge2) (TC = 276 K),which falls below the Gd5(Si1−xGex)4 data shown in figure 3. The low value may be dueto co-existence of the monoclinic and orthorhombic polymorphs in their sample (see above).Thuy [106] also measured �SM for higher Ge content alloys: Gd5(Si1.72Ge2.28), TC = 247 Kand �SM = −251 mJ cm−3 K−1; Gd5(SiGe3), TC = 147 K and �SM = −463 mJ cm−3 K−1;and Gd5(Si0.32Ge3.68), TC = 58 K and �SM = −119 mJ cm−3 K−1. The �SM value forGd5(Si1.72Ge2.28) falls well below, while that for Gd5(SiGe3) lies well above the solid curvedrawn through the Gd5(Si1−xGex)4 data in figure 3. The MCE value for the Gd5(Si0.32Ge3.68)

alloy is much smaller than the earlier value reported by Pecharsky and Gschneidner forGd5(Si0.33Ge3.67), i.e. �SM = −287 mJ cm−3 K−1 [97]. Zhuo et al [107] also measuredthree Ge-rich Gd5(Si1−xGex)4 alloys: Gd5(Si0.75Ge3.25), TC = 108 K and �SM = −377 to−408 mJ cm−3 K−1; Gd5(Si0.6Ge3.4), TC = 92 K and �SM = −315 to −355 mJ cm−3 K−1;and Gd5(Si0.33Ge3.67), TC = 67 K and �SM = −318 to −358 mJ cm−3 K−1. The results forthe first alloy lie close to the Gd5(Si1−xGex)4 curve in figure 3, while that for the second alloyfalls well below this curve. The �SM for the last alloy is larger than the Pecharsky–Gschneidnervalue just cited above for an alloy of the same composition.

The adiabatic temperature rise has also been measured directly on Gd5(Si2Ge2) [108, 109].Giguere et al [108] measured �Tad by the normal technique of rapidly inserting the sampleinto a magnetic field and obtained a value of 8.5 K. Gschneidner et al [109] measured �Tad tobe 16.5 K, when the magnetic field was ramped up to a rate of 20 kOe min−1. The latter valueagreed quite well with the �Tad value calculated from heat capacity measurements made onthe same sample, 16.8 K [109]. This difference in values will be discussed in connection withresults obtained on the La(Fe1−xSx)13 samples, see section 10.1.

As might be expected, the Gd5(Si1−xGex)4 alloys which undergo an FOMT exhibitconsiderable hysteresis. This is discussed in the context of magnetic refrigeration, seesection 11.3.1 and table 8.

5.2.1. Substitution of Gd by other R. Spichkin et al [110] studied the effect of Pr and Tbsubstitutions for Gd in (Gd1−yRy)5Si4. Both Pr and Tb lower TC of Gd5Si4 (346 K) to 292 Kfor Pr and y = 1.0, and to 280 K for Tb and y = 2.5. Pr also lowers the MCE (�SM by ∼25%for a field change of 50 kOe), while Tb may enhance �SM slightly. When Dy replaced Gd inGd5Si4, Xie et al [111] found that TC was lowered in a linear fashion from Gd5Si4 (TC = 338 K)to Dy5Si4 (TC = 140 K) but �SM was only slightly lowered, by ∼8% for (Gd2.5Dy2.5)Si4.

5.2.2. Theory and correlations. A simple phenomenological model was used by von Rankeet al [112] to correlate the influence of external parameters, i.e. magnetic field, pressure


Table 4. The magnetocaloric properties of selected Tb5(Si1−xGex )4 and Dy5(Si1−xGex )4compounds.

−�SM �Tad

TC (mJ cm−3 K−1) (K) DensityCompound Structure type (K) 0–50 kOe 0–50 kOe (g cm−3) Ref.

Tb5Si4 Gd5Si4 225 71 — 7.206 [118]Tb5Si4 Gd5Si4 225 72 6.8 7.206 [119]Tb5(Si3Ge) Gd5(Si2Ge2) 215 50 — 7.506 [106, 119]Tb5(Si3Ge) Gd5Si4 210 63 5.8 7.506 [119]Tb5(Si2Ge2) Gd5(Si2Ge2) 116 97 — 7.589 [106, 119]Tb5(Si2Ge2) Gd5(Si2Ge2) 110 171 — 7.589 [105]Tb5(Si2Ge2) Gd5(Si2Ge2) 105 167 — 7.670 [118]Tb5(Si2Ge2) Gd5(Si2Ge2) 101 117 7.3 7.773 [119]Tb5Ge4 Sm5Ge4 91a 31 — 8.303 [118]

Dy5Si4 Gd5Si4 141 96 — 7.475 [122]Dy5(Si3.5Ge0.5) Gd5Si4 136 91 4.8 7.613 [122]Dy5(Si3Ge) Gd5(Si2Ge2) 65 257 — 7.739 [122]Dy5(Si2.3Ge1.5) Sm5Ge4 56 55 — 7.841 [122]Dy5(Si2Ge2) Sm5Ge4 54 56 — 7.995 [122]Dy5(SiGe3) Sm5Ge4 50 58 — 8.284 [122]Dy5Ge4 Sm5Ge4 46 60 — 8.563 [122]

a Neel temperature.

and volume deformation, on the MCE. Using two empirical parameters they determined thetemperature dependence of �SM for two Gd5(Si1−xGex) alloys, x = 0.5 and 0.57, and foundgood agreement with the experimental results. Casanova et al [113, 114] proposed that �SM

of Gd5(Si1−xGex)4 can be scaled with the transition temperatures, which is tuned by x and theapplied field. The curve of Casanova et al [113, 114] above 125 K is similar to that shown infigure 3 for the Gd5(Si1−xGex)4 alloys.

5.2.3. Other comments. Lewis et al found that the MCE of Gd5(Si1.5Ge2.5) particles couldbe enhanced by ∼11% and ∼20% by coatings of Fe [115] and Al [116], respectively, which isthought to be due to a strain that the coatings impart on the particles. Also see section 11.3.3.

Fujieda et al [117] measured the thermal conductivity (κ) and thermal diffusivity (α) ofseveral magnetocaloric regenerator materials, including Gd5(Si2Ge2), from 4 to 350 K. Bothα and κ of Gd5(Si2Ge2) fall about halfway between those of Gd (higher) and MnAs (lower),with an average value for κ of ∼5.5 W mK−1 between 40 and 325 K.

5.3. Other R5(Si1−xGex)4 systems

5.3.1. Nd5(Si1−xGex)4 alloys. Thuy et al [105] measured the MCE of Nd5(Si2Ge2).They did not report the crystal structure of their sample, but reported TC = 110 K and�SM = −39 mJ cm−3 K−1. The value for �SM falls well below the dashed SOMT lineshown in figure 3.

5.3.2. Tb5(Si1−xGex)4 alloys. After the Gd5(Si1−xGex)4 system, the Tb5(Si1−xGex)4

materials have been the second most studied R5T4 system. The MCE values reported forthe Tb5(Si1−xGex)4 alloys [105, 106, 118–120] are listed in table 4. The Si-rich alloys havethe orthorhombic Gd5Si4 structure and exhibit an SOMT. The MCE values are comparable


with those reported for other materials which have SOMT (see figures 3 and 4). There is somedoubt that the structure reported for Tb5(Si3Ge) by Thuy [106] and Thuy et al [120] as beingthe monoclinic Gd5(Si2Ge2) is correct, especially in view of the result reported by Huang et al[119], i.e. it has the orthorhombic Gd5Si4-type structure and the fact that MCE effect has thetypical caret-like shape which is indicative of an SOMT. If it had the monoclinic structure anFOMT is expected to occur (see below) and the MCE would be two to three times as large andhave a skyscraper-like shape. It is possible that interstitial impurities may have stabilized themonoclinic form for the alloy of Thuy et al (see section 5.1).

Four different investigators have measured the MCE of Tb5(Si2Ge2), and two ofthe studies [106, 120] {the same authors} and [119] report a substantially lower �SM

(−97 mJ cm−3 k−1 and −117 mJ cm−3 K−1, respectively) than the other two [105, 118](�SM = −171 mJ cm−3 k−1 and −167 mJ cm−3 K−1, respectively). An interesting fact isthat the same authors [105, 106, 120] report both the highest and lowest values; presumablythat latest value reported by [106, 120] is the correct one (i.e. �SM = −97 mJ cm−3 K−1).The low �SM values fall on about the SOMT line of figure 3, while the high �SM values lieclose to the RCo2 (FOMT) line of figure 3, point 40. Tegus et al [121] have also measuredthe MCE of ‘Tb5(Si2Ge2)’, but the lattice parameters are much larger than those reported byMorellon et al [118] and Huang et al [119], and it is quite likely that the sample of Tegus et alis richer in Ge than the composition quoted by the authors. Also, the low ordering temperatureof 76 K compared with the values reported by others, 101–116 K (see table 4), also supportsthe proposition it has a higher Ge concentration, i.e. Tb5(Si2−xGe2+x). Their sample has afairly large MCE (�SM = −148 mJ cm−3) and is consistent with an FOMT.

The �SM value for Tb5Ge4 (table 4) is quite low, but that is not unexpected since it ordersantiferromagnetically.

5.3.3. Dy5(Si1−xGex)4 alloys. The MCE of seven alloys in the Dy5Si4 − Dy5Ge4 pseudo-binary has been reported by Ivtchenko et al [122]. Their results are listed in table 4. Thetwo Si-rich alloys which have the Gd5Si4 orthorhombic structure have �SM values whichare slightly higher than the SOMT curve drawn in figure 3. The Dy5(Si3Ge) alloy has themonoclinic Gd5(Si2Ge2)-type structure and undergoes an FOMT. Its �SM value falls close tothe RCo2 (FOMT) line shown in figure 3, point 41.

The four Ge-rich alloys which have the orthorhombic Sm5Ge4-type structure order at afairly low, nearly constant temperature (table 4). Their �SM values fall well below the SOMTline of figure 3.

5.3.4. Ho5(Si2Ge2). The MCE of Ho5(Si2Ge2) (density is 8.239 g cm−3), which wasmeasured in very high-magnetic fields, is the only Ho5(Si1−xGex) alloy studied to date. Thiscompound orders antiferromagnetically at ∼25 K and has the Sm5Ge4 orthorhombic typestructure [123]. The authors report �SM = −482 mJ cm−3 K−1 for a 0–380 kOe field change.No lower field MCE values were given, and so it is difficult to compare this value with the�SM values reported for other R5(Si1−xGex)4 compounds. Presumably the �SM value for a0–50 kOe field change is greater than −63 mJ cm−3 K−1—the value obtained assuming �SM

varies linearly with field; but as shown in figure 2(a), �SM versus H shows considerablecurvature for most materials and one would expect the low field �SM to be higher than a valueobtained by a linear interpolation.

5.4. Sn containing R5T4 compounds

Ryan et al [124] reported that Gd5Sn4, which has the Sm5Ge4 orthorhombic type structure,exhibits a GMCE (�SM = −336 mJ cm−3 K−1) at TC = 82 K. This �SM value is significantly


smaller than the Gd5(Si1−xGex) values, but somewhat larger than those of the RCo2 phases,see figure 3, point 45.

Campoy et al [125] have reported on the MCE in Gd5(Si2Sn2). Unfortunately theseauthors did not report any structural data. However, Wang et al [126] reported that a phase ofthis composition had the Gd5(Si2Ge2) monoclinic type structure and listed the lattice constants.Using these lattice constants we were able to calculate the �SM value in volumetric units. Thevalue for the Gd5(Si2Sn2) compound (density is 8.850 g cm−3) is −37 mJ cm−3 K−1, which issomewhat smaller than the SOMT line of figure 3.

6. Mn-based compounds

A number of different metallic manganese compounds have interesting MCE behaviours.Several of them have quite large MCE values (e.g. some of the MnAs-based andMnFeP0.45As0.55 compounds); others exhibit fairly strong negative MCEs (e.g. Mn3GaCalloys); and others have rather unique behaviours which are associated with decoupledstructural and magnetic transitions which are tens of Kelvins apart (e.g. the Ni2MnGa Heusleralloys). In addition, there are the oxide manganites which are discussed in section 8.

6.1. Mn(As1−xSbx) alloys

The base material MnAs (density is 6.799 g cm−3) undergoes a coupled structural/magneticFOMT at 318 K. The ferromagnetic hexagonal NiAs-type structure transforms to theparamagnetic orthorhombic MnP-type structure upon heating or demagnetizing. The MCEvalues are quite large and are considered to be in the GMCE class of magnetic refrigerants:�SM = −218 mJ cm−3 K−1 and �Tad = 13 K for a 0 to 50 kOe field change [56] at TC. The�SM value lies above the Gd5(Si1−xGex)4 FOMT line (figure 3, point 36), while the �Tad

value is located near the value for La(Fe11.1Si1.56)H1.5 data for a 0 to 50 kOe field change point(figure 4, point 32). The field dependence of �SM is shown in figure 2(a) along with severalother materials. It is seen that the �SM response to magnetic fields is the best among thepotential magnetic refrigerant materials (figure 2(a)). The corresponding field dependence of�Tad is presented in figure 2(b), where it falls close to Gd metal, but is somewhat less thanthe field dependence of Gd5(Si2Ge2). There is, as expected for a substance undergoing a first-order structural transition, a significant hysteresis of 6.5 K [127], also see section 11.3.1 andtable 8. Fujieda et al [117] measured the thermal conductivity (κ) and thermal diffusivity (α)of several magnetocaloric regenerator materials, including MnAs, from 4 to 350 K. Both theα and κ values of MnAs are the lowest of the five materials studied. The thermal conductivityslowly increases with increasing temperature from 1.2 W mK−1 at 25 K to 2.0 W mK−1 at TC

(318 K), and then it rises more rapidly to 2.7 W mK−1 at 350 K.Wada et al [56, 127, 128] have studied the effect of substituting Sb for As in MnAs. They

note that Sb stabilizes the NiAs-type structure when x � 0.1, and the FOMT changes to SOMT,which results in a reduction of �SM and �Tad. Sb also lowers the TC (see figure 6(a)). Theconcentration dependence of �SM is shown in figure 6(b). As is seen, TC decreases in an almostlinear manner until x ∼= 0.25, and then it seems to be levelling-off, while �SM drops slowlywith the initial substitution of Sb for As, maintaining its high �SM value until x ∼= 0.20. TheMnAs1−xSbx system behaves differently from most families of magnetic refrigerant materialsin that �SM decreases with decreasing TC, see figure 3, and as a result the high value for �SM

of MnAs falls below those of the Gd5(Si1−xGex)4 family at ∼290 K and the MnFeP1−xAsx

family at ∼235 K when Sb is substituted for As.


Figure 6. The Curie temperature versus composition for the Mn(As1−xSbx) alloys (a), and theisothermal entropy change for a 0–50 kOe field change versus composition for the Mn(As1−xSbx)

alloys (b).

The effect of adding excess Mn to Mn1+yAs0.75Sb0.25 was to lower the transition from 234 Kat y = 0 to 204 K for y = 0.05, but �SM essentially remained the same (∼−150 mJ cm−3 K−1)for a field change of 0 to 10 kOe [129]. For higher concentrations, i.e. y = 0.08 and 0.11,TC continues to drop, but �SM rapidly decreases by a factor of 10 to −14 mJ cm−3 K−1 fory = 0.08 and to nearly zero for y = 0.11.

The MCE properties of MnAs1−xSbx for 0.1 � x � 0.2 are outstanding and these alloysare among the leading candidates as near room temperature magnetic refrigerant materials;however, the high vapour pressure of As (boiling point 876 K [603˚C]) makes it difficult toprepare large quantities (tons) of MnAs in an economical way. MnAs1−xSbx is prepared bysealing the three components in a quartz tube and sintering at 873 to 1073 K for one week,then crushing the reaction products and resintering at 1073 K for another week [56, 127, 129].A second problem is the fact that As is a governmentally regulated poison, which means specialhandling facilities would be required for preparing the MnAs1−xSbx material, and specialenvironmental regulations will need to be met to place such cooling devices into commerce.Also see section 11.3.1.

6.2. MnFe(P1−xAsx) alloys

Recently, Tegus et al [130] pointed out that MnFeP0.45As0.55 (density is 7.256 g cm−3) has someinteresting MCE properties, �SM = −132 mJ cm−3 K−1 for a 0 to 50 kOe field change, and anordering temperature of 307 K. The �SM and TC values place it close to the highest orderingGd5(Si1−xGex)4 alloy [point 31 at the end of the Gd5(Si1−xGex)4 (FOMT) line] shown infigure 3, point 37, indicating that MnFeP0.45As0.55 is a competitive magnetic refrigerant for nearroom temperature applications. The effect of changing the P to As ratio on the MCE and TC wasreported by Tegus et al [88] in a second paper. As the As content (x) decreases, TC is lowered(figure (7(a)) and �SM generally increases as x decreases and seems to peak at x = 0.35 beforefalling off for smaller x (figure (7(b)). The increase in �SM as TC decreases is not nearly as largeas that for the Gd5(SixGe1−x)4 alloys; atTC = 215 K it is about two-thirds the value of that of the


Figure 7. The Curie temperature versus composition for the MnFe(P1−xAsx) alloys (a), and theisothermal entropy change for a 0–50 kOe field change versus composition for MnFe(P1−xAsx)

alloys (b).

corresponding Gd5(SixGe1−x)4 alloy (−230 versus −310 mJ cm−3 K−1, see figure 3). All thealloys exhibit an FOMT, and there is a fairly uniform hysteresis of 4 K or 7 kOe for 0.25 � x �0.65 (also see section 11.3.1 and table 8). The effect of Mn substitution for Fe hardly changesTC but increases �SM, i.e. for (Mn1+yFe1−y)P0.5As0.5 (density is 7.267 g cm−3 for y = 0.1), TC

is lowered by 2 K at y = 0.1 but �SM is increased by ∼40% from −145 to −203 mJ cm−3 K−1

[131] for a field change of 0 to 50 kOe. On the other hand, the substitution of Ge for As, i.e.MnFe(P0.5As0.5−xGex), has just the opposite effects—a large increase of TC from 282 K forx = 0 to 570 K for x = 0.5, and a reduction of the MCE [132]. The only �SM values reportedwere for x = 0 (density is 7.203 g cm−3) and x = 0.06 (density is 6.575 g cm−3). The MCEwas reduced by more than 54% from −119 to −55 mJ cm−3 K−1 for a field change of 20 kOe.

Tegus et al [133] studied the effect of Cr and Co substitutions for Fe in MnFe(P1−xAsx).For the Mn(Fe1−xCrx)P0.47As0.53 alloy (TC = ∼ 305 K), Cr lowers both TC and �SM, and theFOMT changes to an SOMT: at x = 0.02, TC = ∼ 275 K and �SM is lowered by ∼25% for�H =20 kOe, and at x = 0.09, TC =∼190 K and �SM is lowered by ∼65% for �H =20 kOe.For the alloy Mn(Fe1−xCox)P0.5As0.5, a 10% substitution of Co for Fe (x = 0.1) lowers TC

from 282 to 260 K and the �SM value by ∼55% for �H = 20 kOe.The preparation of the MnFeP1−xAs alloys is similar to that of the MnAs1−xSbx alloys.

For the former alloys, the components were sealed in Mo tubes and heated to 1273 K for120 h followed by homogenization at 923 K for another 120 h, and then slow-cooled to 295 K.Although these alloys have good MCE properties, the high vapour pressure of As and itstoxicity are obstacles in the utilization of MnFeP1−xAsx alloys in commercial devices, see theend of section 6.1 for additional comments. In addition, P presents some special problemsincluding its high vapour pressure (boiling point 550 K [277˚C] for white P and 704 K [431˚C]for red P) and handling requirements. Also see section 11.3.1.

6.3. Ni–Mn–Ga Heusler alloys

The Heusler alloys have the ideal formula of Ni2MnGa, but most alloys have variations ofseveral atomic per cent from the ideal 2 : 1 : 1 composition for each component. This material


exhibits both a structural transformation (Tm) between ∼175 and ∼220 K and an FM to PMtransition (TC) between ∼315 and ∼380 K, depending upon the Ni : Mn : Ga ratios. It isinteresting to note that there is an inverse relationship between Tm and TC, i.e. the smaller Tm,the larger TC and vice versa. The structural transformation is first order as the L12-type cubicstructure changes to a tetragonal structure on cooling. Both phases are ferromagnetic, but thecubic modification is the magnetically softer phase. There has been considerable research onthese alloys because of their unusual properties: large magnetostrictions, superelasticity andferromagnetic shape memory effect. However, it was not until 2000 that the MCE propertieswere first reported by Hu et al [134], and since then several other papers have been published[88, 135–139]. All the studies indicate that there is a negative MCE associated with the first-order martensitic transition, which is quite large at low-magnetic fields and decreases as themagnetic change becomes larger. For example, Marcos et al [136] finds the maximum valueof �SM occurs at 13 kOe with �SM = 90 mJ cm−3 K−1 for single crystal Ni49.5Mn25.4Ga25.1

(Tm = 177 K and density is 8.2 g cm−3) with the magnetic field applied along the [100]direction. At the FM–PM transition the MCE is normal, i.e. �SM has a negative value. The�SM value is small at low fields and increases rapidly with increasing field. For example,Pasquale et al [137] report that �SM increases from −15.6 to −30.0 to −144 mJ cm−3 K−1

for magnetic field changes of 0 to 10, 0 to 20 and 0 to 50 kOe, respectively, in single crystalNi51.0Mn27.9Ga21.1 (density is 8.0 g cm−3) with H applied along the [100] direction. Theonly reported �Tad value was given by Aliev et al [138] who found �Tad = 1.2 K for afield change of 0 to 26 kOe at the FM–PM transition temperature of 340 K for polycrystallineNi54.8Mn20.2Ga25.0.

More recently Albertini et al [139] reported an extremely large �SM value(−121 mJ cm−3 K−1) for Ni54.8Mn20.2Ga25.0 (density is 7.8 g cm−3) at its TC (351 K) for a0 to 18 kOe field change. This is the largest value reported to date for a Ni2NiGa Heusleralloy for a �H < 50 kOe. At about the same time Zhou et al [140] reported a large�SM value for an alloy of nearly the same composition, i.e. Ni55.2Mn18.6Ga26.2 (density is8.247 g cm−3). They obtained a value of −168 mJ cm−3 for �H = 50 kOe at TC = 317 K,and −78 mJ cm−3 K−1 for �H = 15 kOe. The �H = 50 kOe value (point 46 in figure 3) isslightly higher (more negative) than the �SM values reported for the La(Fe13−xSix)Hy alloys.These data suggest that the Ni–Mn–Ga alloys near the Ni55Mn19Ga26 composition might begood magnetic regenerator alloys for refrigerators/heat pumps operating between ∼300 and∼350 K. The �SM peak for Ni55.2Mn18.6Ga26.2 for �H = 50 kOe, however, is quite sharp,only 5 K wide at half of the peak height maximum [140], and this may limit the usefulness ofthe Ni–Mn–Ga Heusler alloys as a near room temperature magnetic refrigerant. For example,Gd5(Si2Ge2) and La(Fe11.44Si1.56)H1.5, which have �SM peak height maxima comparable withNi55.2Mn18.6Ga26.2, have peak widths of 14 K [51] and 10 K [141] at half of the peak heightmaximum, respectively. The Ni54.8Mn20.2Ga25.0 alloy exhibits a temperature hysteresis of 7 K,confirming this compound undergoes FOMT [139]. Also see section 11.3.1 and table 8.

The Ni–Mn–Ga Heusler alloys are fairly easy to prepare—the stoichiometric amounts ofthe desired alloy are just arc melted. However, to ensure that the samples are homogeneousthey are heat treated in an inert atmosphere for eight to ten days at 850˚C [140].

6.4. Miscellaneous compounds

6.4.1. Mn5Si3-based and Mn5Ge3-based alloys. The MCE of Mn5Si3 was studied by Teguset al [88]. Mn5Si3 exhibits two FOMTs: one at 66 K between a non-collinear AFM and acollinear AFM state, and one at 99 K between the collinear AFM and PM. The �SM values forMn5Si3 at the lower FOMT are presented in table 5. There is no MCE peak at the upper FOMT


Table 5. The magnetocaloric properties of selected Mn-containing intermetallic compounds.



Mn1.82V0.18Sb 242 — 39 — — 7.106 [144]Mn1.95Cr0.05Sb 198 41 49 — — 7.039 [88]Mn3GaC 160a −103 −109 −5.5 −5.5 6.933 [145]Mn2.97Co0.03GaC 130a — −96 — — 6.937 [146]Mn2.95Co0.05GaC 100a — −88 — — 6.939 [146]Mn5Si3 62.5a −5.1 −24.5 — — 5.987 [88]DyMn2Ge b

2 40 85 108 5.2 7.2 8.033 [148]DyMn2Ge b

2 35 58 −0.5 3.8 −2.4 8.033 [148]

a Neel temperature.b Single crystal.

(99 K), but a small, normal MCE peak is observed at ∼68 K, i.e. �SM = −8 mJ cm−3 K−1 fora 0 to 50 kOe field change.

The �SM values have been determined for a number of (Mn5−xFex)Si3 alloys (x =0, 3, 4 and 5) by Songlin et al [142]. The high Mn-containing alloys (x = 0 and 3) areantiferromagnetic and the Fe-rich phases (x = 4 and 5) are ferromagnetic. The substitutionof Fe also raises the ordering temperatures: TN1 = 64 K and TN2 = 100 K for Mn5Si3 toTC = 375 K for Fe5Si3. The MCE for Mn5Si3 exhibits a sharp peak slightly above TN1 (70 K); abroad peak between TN1 and TN2 (centred at 175 K) for (Mn2Fe3)Si3; and a caret-like peak at TC

for both (MnFe4)Si3 and Fe5Si3. In any event the |�SM| values lie well below the dashed SOMTin figure 3, e.g. −25 mJ cm−3 K−1 for �H = 50 kOe for Mn5Si3 (density is 5.987 g cm−3).

Songlin et al [143] also measured the MCE in Mn5Ge3 (density is 7.241 g cm−3) whichorders at 298 K. The �SM value for a 0 to 50 kOe field change is −67 mJ cm−3 K−1, whichis comparable with the SOMT values reported for a number of substances which order near300 K (see figure 3). The authors also studied the substitution of Sb for Ge, Mn5(Ge1−xSbx)3,and noted that TC is increased to 312 K for x = 0.1 and �SM is lowered to −40 mJ cm−3 K−1

for x = 0.1.

6.4.2. (Mn1−xMx)2Sb alloys. The MCE of two (Mn1−xMx)2Sb compounds (where M isa transition metal) have been studied. These compounds have the tetragonal Cu2Sb-typestructure. Tegus et al [88] found that (Mn1.95Cr0.05)Sb orders at 198 K with a modest MCE,see table 5, and essentially falls on the dashed SOMT line of figure 3.

Zhang and Zhang [144] reported on their investigation of (Mn1.82V0.18)Sb, which ordersat 242 K. The MCE value for a 0–50 kOe field change is given in table 5, and it lies slightlybelow the dashed SOMT line shown in figure 3.

6.4.3. Mn3GaC-based materials. Tohei et al [145] studied the MCE of Mn3GaC whichexhibits an FOMT from an AF to FM state with increasing temperature, which is the opposite ofwhat occurs in most magnetic materials. As a result Mn3GaC exhibits a fairly large negativeMCE, see table 5. The �SM value of this compound falls well above the dashed SOMT lineof figure 3 and would lie on an extension of the RCo2 FOMT solid line up to 160 K.

Tohei et al [146] also studied the influence of Co substitutions for Mn. They found thatas the Co concentration increases both TC and �SM are lowered, see table 5.

6.4.4. Fe2Mn(Si1−xGex). The magnetic properties of Fe2MnSi0.5Ge0.5 (density is7.624 g cm−3), including the MCE, were measured by Zhang et al [147]. They found


TC = 260 K and �SM = −12.7 mJ cm−3 K−1 for a field change of 50 kOe. This �SM valuefalls far below the SOMT line established by many other intermetallic compounds shown infigure 3.

6.4.5. DyMn2Ga2. Wada et al [148] have studied the MCE in single crystalline DyMn2Ge2,which has two FOMTs at 36 and 40 K, and a metamagnetic transition above 40 K, and as aresult the MCE behaviour is complex. A sharp, normal caret-like peak is observed at 35 K for�H = 20 kOe, but for �H = 50 kOe a negative MCE peak is observed, see table 5. However,above 40 K a broad table-like MCE peak is observed which is approximately constant between40 and 47 K for �H = 20 kOe, and between 40 and 55 K for �H = 50 kOe, see table 5. The�SM value at 40 K for �H = 50 kOe is smaller than that of the dashed SOMT line in figure 3,but the �Tad value is consistent with the values shown in figure 4 for �H = 50 kOe and aresignificantly higher for �H = 20 kOe.

7. La(Fe13−xMx)-based compounds

7.1. Unsubstituted La(Fe13−xSix)

The existence of the La(Fe13−xMx) intermetallic compounds has been known since the late1960s [149, 150], and their magnetic properties were initially characterized in the mid-1980s[151, 152]. The M element is usually Si or Al, but other metals such as Ga have been substitutedfor Fe. The LaFe13 phase does not exist; as a matter of fact no intermetallic compounds formin the La-Fe binary system, and La and Fe form immiscible liquids at the Fe-rich side between∼8 and 20 at% La above 1460˚C [153]. Thus it is necessary to add other elements to theLa–Fe alloys to form the intermetallic La(Fe13−xMx) phases. The La(Fe13−xMx) phases havethe cubic NaZn13 D23-type structure [149–152] with a lattice parameter of ∼11.5 Å, andtetragonal distortions have been reported for some compositions.

Palstra et al reported some unusual magnetic properties for the La(Fe13−xSix) [151]and La(Fe13−xAlx) [152] phases. For the La(Fe13−xSix) alloys TC increases from 198 Kat x = 1.5 to 262 K at x = 2.5, while the saturation magnetic moment decreases from 2.08to 1.85 µB/Fe as x increases from 1.5 to 2.5. Furthermore, they noted a lattice softeningnear the Curie temperature which they thought was associated with the Invar effect [151].For the La(Fe13−xAlx) system Palstra et al [152] found that for x � 1.8, a low temperatureantiferromagnetic state which exhibited an extremely sharp metamagnetic transition in anapplied magnetic field of a few kilooersteds, with a large hysteresis for field up versus fielddown. In 1999, Fujita et al [154] observed a large volume change (∼1.5%) in La(Fe11.44Si1.56)

just above the Curie temperature (195 K) during magnetization measurements in magneticfields as low as 10 kOe. They claimed this behaviour was due to an IEM transition. This largevolume change and the shape of the magnetization curves suggested that this alloy might havesome interesting magnetocaloric properties. Indeed, a year later, Hu et al [155] and Zhang et al[156] reported that La(Fe11.47Co0.23Al1.3) and La(Fe10.6Si2.4), respectively, exhibit a modestMCE. Subsequently a number of investigators have reported large MCE entropy changes inthe La([Fe,T]13−xSix) systems which are discussed below.

In 2001, Hu et al [157] were the first to find the GMCE in the La(Fe1−xSix)13 alloys.They reported that La(Fe11.4Si1.6) (density is 7.229 g cm−3), which orders at 208 K, had an�SM value of −140 mJ cm−3 K−1 for a magnetic field change of 0 to 50 kOe. They alsofound that when more of the Fe is replaced by Si the magnetic ordering temperature is raisedand the MCE is substantially reduced: for La(Fe10.4Si2.6), TC = 243 K and �SM is aboutsix times smaller than that of La(Fe11.4Si1.6) for a 0 to 20 kOe field change. In 2002 only


Figure 8. The Curie temperature versus Si content, x, for the La(Fe13−xSix) alloy system (a), and�SM for a 0 to 50 kOe field change versus Si content, x, for the La(Fe13−xSix) alloy system (b).

Reference legend10—Hu et al [157] 14—Wang et al [160] 18—Liu et al [164]11—Wen et al [158] 15—Chen et al [161] 19—Anh et al [165]12—Fujita et al [141] 16—Hu et al [162] 20—Wang et al [166]13—Hu et al [159] 17—Chen et al [163]

three papers [52, 158, 159] were published on the MCE in the La(Fe1−xSix) alloys, but allthat changed in 2003 when eight additional papers [141, 159–166] were published in variousjournals. The TC and �SM values are plotted as a function of x in figure 8. It is seen that theCurie temperature increases monotonically from ∼180 K at x = 1.3 to ∼250 K at x ∼= 2.6(figure 8(a)). However, the TC value reported for La(Fe10.2Si2.8) [158] is significantly outof line with the rest of the reported data. It should be noted that Wen et al [158] report TC

values for two other alloys (x = 2.4 and 2.6) which are consistent with the results reported byother investigators [52, 141, 159–166]. The TC anomaly for x = 2.8 may be due to a changein the magnetic properties of the La(Fe13−xSix) phases for x > 2.6 compared with those forx < 2.6. This is evident in the temperature dependences of the magnetization and the MCEof the x = 2.8 alloys compared with those for x = 2.4 and 2.6 [158].

The MCE as a function of x (figure 8(b)) shows that the �SM drops rather rapidly withincreasing x, i.e. from ∼−215 mJ cm−3 K−1 at x = 1.3 to ∼−100 mJ cm−3 K−1 at x = 1.8.For x > 1.8, �SM is small and seems to level off at ∼−40 mJ cm−3 K−1. The value reportedby Anh et al [165] for x = 1.56 seems to be anomalously low compared with the otherreported values for the La(Fe13−xSix) alloys. The �SM versus T curves of the low x valuealloys (x � 1.7) are sharp and have a skyscraper-like shape for low field changes (0 to 20 kOe),but broaden on the high temperature side of the MCE peak for large magnetic field changes(greater than 0 to 30 kOe). This behaviour is typical for an FOMT, e.g. see Fujieda et al [52].However, for large x, i.e. >2.4, the �SM versus T curves have the caret-like shape, which istypical for an SOMT, e.g. see Wen et al [158]. For 1.7 � x � 2.4 the MCE peaks have acaret-like shape, but the heights are fairly large compared with those for x � 2.4.

The magnetization curves for an increasing field and for a decreasing field of theLa(Fe13−xSix) alloys for small x, i.e. ∼1.3, have a hysteresis between 4 [141] and 6 kOe [162],


which is consistent with the magnetic transition being first order. The width of the hysteresisis ∼2 times smaller than that typically observed in the Gd5(SixGe4−x) phases, which is about10 kOe [167]. As expected, for those alloys which exhibit an SOMT there is no observablehysteresis, i.e. for alloys with x � 2.4 [158]. Hu et al [162] report a 3 K hysteresis in theirdirect measurement of �Tad in a magnetic field of 14 kOe between an increasing field anddecreasing field, which is about one-third of that observed in Gd5(SixGe4−x) alloys. Also seesection 11.3.1 and table 8.

Heat capacity measurements of the La(Fe13−xSix) alloys for x = 1.30, 1.43 and 1.56 inmagnetic fields of H = 0, 10, 20, 30 and 50 kOe by Fujita et al [141] show a sharp narrow peakat the ordering temperature, which shifts towards higher temperatures and becomes broaderwith increasing fields. Again, this confirms that the paramagnetic/ferromagnetic transition isfirst order.

X-ray powered diffraction measurement by Fujieda et al [168] of La(Fe11.4Si1.56) as afunction of temperature from 270 to 300 K showed that the crystal structure did not change asthe sample was swept through the Curie temperature (280 K) but that there was a significantshift of the x-ray diffraction peak, confirming the large volume change (∼1%) observed in thethermal expansion measurements.

The first-order, purely magnetic transition and associated anomalous behaviours, giantmagnetostrictions and the GMCE in La(Fe13−xSix) for x < 1.7, are due to an IEM transition,i.e. a field induced magnetic transition from the paramagnetic state to the ferromagneticstate above the respective Curie temperature [52, 141, 168, 169]. Yamada and Goto [169]showed that when spin fluctuations were included in the Ginzburg–Landau phenomenologicaltheory, the GMCE would be expected in itinerant electron metamagnets when the coefficientof the M4 term in the Landau energy expansion with respect to the magnetization is large andnegative, which it is in the La(Fe13−xSix) phase with x � 1.7. Also see section 2.

Although the low x value La(Fe13−xSix) compounds exhibit large �SM values, it doesnot follow that these materials will necessarily have large �Tad values; in general many ofthe compounds reported here up to now to have large �SM values do not have large �Tad

values [170]. The Japanese scientists [52, 141] have calculated �Tad from heat capacitymeasurements and find them to be substantial, 8.6–12.1 K, for a magnetic field change of 0 to50 kOe, and comparable with those of the Gd5(SixGe4−x) phases which have TC’s �200 K.But for TC > 220 K, the Gd5(SixGe4−x) phases have �Tad values which are by 25–50% largerfor the same field changes, see figure 10 of [171] (also unpublished data by the authors). Directmeasurements of �Tad have been reported for three La(Fe13−xSix)-based alloys [141, 162, 172]and these are ∼25% lower than the indirect values of �Tad calculated from heat capacitymeasurements; this is discussed in more detail in section 7.7.

Fujita et al [141] noted that after repeated thermal cycles (the number was not specified)there was no observable change in the MCE values. This is consistent with the fact thatthere is no crystal structure change associated with IEM transitions, only a large volumechange.

It should be pointed out that all the La(Fe13−xSix) samples prepared to date, includingthose in which La has been substituted for by Nd, and Fe by Co and Mn, and those alloys towhich M and C have been added (see sections 7.3–7.6), are two phase alloys containing upto 5% α-Fe. This is not surprising considering that La and Fe form immiscible liquids (seeabove, section 7.1). Even long term anneals, up to 30 days, do not eliminate the second phaseα-Fe. The annealing temperatures varied from 1000˚C to 1050˚C, and the shortest annealingperiod was 6 days.

Fujieda et al [117] measured the thermal conductivity (κ) and thermal diffusivity (α) ofseveral magnetocaloric regenerator materials, including La(Fe11.44Si1.56)Hy for y = 0 and


1.0, from 4 to 350 K. The κ of the two alloys rises rapidly with increasing temperature from∼1.5 W mK−1 at 25 K to 11.4 W mK−1 at 350 K. This behaviour is in contrast with the othermagnetic refrigerant materials which generally do not change much with temperature. Thevalues for the y = 1.0 sample are 10% to 20% higher than those for y = 0.

7.2. Mossbauer and neutron diffraction studies

Liu et al [164] carried out x-ray and Mossbauer spectroscopy studies on the La(Fe13−xSix)alloys for x = 1.6, 2.0 and 2.6. They found that the La–Fe(2) distance decreased whilethe Fe(1)–Fe(2) distance increased, and the Fe(2)–Fe(2) distance remains unchanged as Si issubstituted for Fe, i.e. as x is increased (the La atoms are located on the 8a sites, Fe(1) onthe 8b sites and Fe(2) on the 96i sites of the NaZn13-type structure). They stated that thedifferent nature of the magnetic transitions (first order for x = 1.6 and 2.0 and second orderfor x = 2.6) with changing x originates from the spatial distribution of the Si atoms whichonly substitute for the Fe(2) atoms. They conclude that the replacement of the La–Fe pairsby La–Si pairs improves the structural stability because the average Fe–Fe distance increaseswith increasing x (although the lattice parameter decreases with increasing x). This largerFe–Fe distance enhances the positive exchange interaction, which accounts for the increase ofTC with increasing x.

A Mossbauer study of La(Fe10.53Si2.47) by Hamdeh et al [173] confirmed the resultsreported by Liu et al [164] concerning the substitution of Si for the Fe(2) atoms. Furthermore,Hamdeh et al conclude from quadrupole splitting and isomer shift there is a redistribution of 3delectrons of Fe between the spin-up and spin-down subbands which reduces the Fe magneticmoment.

Neutron diffraction studies by Wang et al [166] are in disagreement with the Mossbauerresults [164, 173] regarding the substitution of Si for Fe in the La(Fe11.4Si1.6) alloy. Wanget al find that the Si atoms, within experimental error of a Rietveld refinement, randomlyoccupy both the Fe(1) and Fe(2) sites. Furthermore, they find that all the spins are alignedferromagnetically and the magnetic moment, p, on the Fe(1) atoms is smaller than that onthe Fe(2) atoms: at 185 K (TC = 193 K) pFe(1) = 1.3 µB versus pFe(2) = 1.7 µB; and at 2 KpFe(1) = 1.54 µB versus pFe(2) = 2.16 µB. Wang et al also found a large volume expansion(∼1%) when the alloy orders magnetically, confirming the earlier observation of Fujita et al[154], and found that the paramagnetic and ferromagnetic phases coexist near TC.

7.3. Substitution for La

Anh et al [165] found that Nd substitution for La in (La1−zNdz)(Fe11.44Si1.56) (density is7.233 g cm−3) up to z = 0.4 lowered the lattice parameter linearly and slowly raised TC from210 to a maximum of 215 K at z = 0.3, which dropped to 205 K at z = 0.4 and lowered theMCE from �SM = −91 mJ cm−3 K at z = 0 to −68 mJ cm−3 K at z = 0.3 for a 0 to 50 kOefield change. These results indicate the substitution of Nd for La has an adverse effect on theMCE of the La(Fe11.46Si1.56) compound.

7.4. Substitution for Fe

Four studies have been carried out on the influence of Co substitutions for Fe in variousLa(Fe13−xSix)-based alloys: Hu et al [174] studied the La(Fe11.2Co0.7Si1.1) alloy (density is7.390 g cm−3), Liu and Altounian [175] the La(Fe1−zCoz)11.4Si1.6 series of alloys for z = 0 toz = 0.10; and Hu et al [159] the La(Fe1−zCoz)11.2Si1.8 series of alloys for z = 0 to z = 0.08. In


all cases, Co additions significantly and linearly increase TC from ∼210 to ∼330 K at z = 0.10;but �SM is lowered from −93 to −50 mJ cm−3 K−1 at z = 0.08 for La(Fe1−zCoz)11.2Si1.8

[159] and from ∼−150 to ∼−80 mJ cm−3 K−1 at z = 0.07 for La(Fe1−zCoz)11.4Si1.6 [175].Liu et al [176] studied the magnetic transitions in the La(Fe1−zCoz)11.4Si1.6 alloys (where0 � z � 0.08) by dc magnetization measurements and Mossbauer spectroscopy andconcluded that Co substitution for Fe (z � 0.02) drives the first-order ferromagnetic–paramagnetic transition towards second order, eliminating IEM transition.

Wang et al [160] found that the substitution of small amounts of Mn for Fe inLa(Fe1−zMnz)11.7Si1.3 (where 0 � z � 0.03) has a large effect on TC and the MCE.The Curie temperature is rapidly lowered in a nearly linear fashion from 188 K at z = 0 to127 K at z = 0.03. The initial substitution of Mn (z = 0.01) barely changes the MCE, i.e.|�SM| decreases from −190 to −187 mJ cm−3 K−1. However, for larger amounts of Mn, theMCE drops off quite rapidly to −151 mJ cm−3 K−1 for z = 0.02 and −123 mJ cm−3 K−1 forz = 0.03. The influence of Mn on TC is just the opposite of Co substitution, while the twoalloying agents have a similar effect on the MCE: it is lowered, but the �SM versus z plots aresomewhat different.

7.5. Addition of interstitial elements—hydrogen

To date only H and C additions to La(Fe13−xSix) have been studied, and the behaviours of thesetwo interstitial elements are different. Both interstitials raise TC, but C additions drasticallylower �SM, while for H additions, �SM slightly decreases while �Tad exhibits a large increase.

The hydrogen addition studies were carried out by Chen et al [177] on La(Fe11.5Si1.5)Hy

and by Fujita et al [141] and Fujieda et al [168] on various La(Fe13−xSix)Hy samples. Theresults reported by Chen et al [177] are based on magnetization measurements, while Fujitaet al determined the MCE from heat capacity measurements as a function of temperature andmagnetic field and from magnetization measurements [141] and by direct measurement of�Tad [172]. The Curie temperature dependence on y is shown in figure 9(a), where it is seenthat TC increases in a linear fashion with increasing y, and is essentially independent of theFe to Si ratio. The hydrogen concentration dependences of the MCE (both �SM and �Tad)

are shown in figure 9(b), where �SM slightly decreases with increasing y (ignoring the lowvalues reported by Chen et al for y = 0.3 to y = 1.5), but �Tad increases by about 50% wheny = 1.5 compared with y = 0. According to Fujita et al [141], this non-parallelism between�SM and �Tad is due to the fact that the lattice heat capacity, CL, remains essentially constantas y increases but that TC increases with y, and thus CL/TC decreases, and since �Tad ∝ T/C

(see equation (4) of [141]), �Tad rises rapidly with increasing H content. However, when oneexamines the �Tad values for a 0 kOe to 20 kOe magnetic field change, �Tad remains essentiallyconstant, i.e. = 6.5 K, 6.0 K, 6.2 K and 6.8 K for y = 0, 0.5, 1.0 and 1.5, respectively. Thisbehaviour is more or less consistent with the nearly constant �SM value for both the 0 to20 kOe and 0 to 50 kOe field changes. Thus the explanation for the non-parallelism may bemore complicated than what was proposed by the authors of [141].

The results reported for �SM versus y by Chen et al [177] (see squares in figure 9(b)) area little difficult to understand in view of the results of Fujita et al [141] (noted above and thecircles in figure 9(b)), especially since the y = 0 and y = 1.8 values for �SM reported by Chenet al are in good agreement with the data of Fujita et al. No explanation was given by Chen et alfor this discrepancy. As seen in figure 9(a) all the results reported by the two groups for thevariation of TC versus y are in excellent agreement, and thus we conclude that the alloys, whichhave anomalously low �SM values, have the correct hydrogen content. Thus the anomaly isnot due to an incorrect hydrogen concentration. A possible explanation is that the starting


Figure 9. The Curie temperature versus the hydrogen concentration, y (a) and the adiabatictemperature rise (top) and the magnetic entropy change (bottom) versus the hydrogen concentration,y (b) for the La(Fe13−xSix)Hy alloy system.

Table 6. The Curie temperature, magnetic entropy change and adiabatic temperature rise for someLa(Fe13−xSix)Hy alloys for a magnetic field change of 0–50 kOe.

−�SM DensityCompound TC (K) (mJ cm−3 K−1) (g cm−3) �Tad (K)

La(Fe11.7Si1.3)H1.1 287 222 7.156 15.4La(Fe11.57Si1.43)H1.3 291 200 7.139 12.8La(Fe11.44Si1.56)H1.0 274 165 7.164 11.1

La(Fe13−xSix) master alloys for making the hydrogen containing alloys are of two slightlydifferent Fe to Si ratios. That is, the master alloy for y = 0 and 1.8 had a composition closeto La(Fe11.44Si1.56) and that for the five alloys with y = 0.3 to 1.5 has a composition close toLa(Fe11.3Si1.7). As discussed below, and shown in table 6, the Fe to Si ratio is more criticalthan the hydrogen content in determining �SM.

As seen in figure 9(a), there is an excellent correlation between TC and the hydrogencontent, y, regardless of the Fe : Si ratio; and for a fixed Fe : Si ratio, �Tad and �SM show adependence on y (figure 9(b)). A closer examination of the available data indicates that both�Tad and �SM have a strong dependence on the Fe : Si ratio at a fixed y value. This is quiteevident as shown in table 6 for the three La(Fe13−xSix)Hy , where y ∼= 1.1, the higher the Fecontent the larger �SM and �Tad. This is also consistent with the data obtained for these alloyswhere y = 0, see figure 8(b).

The thermal conductivity and thermal diffusivity of La(Fe11.44Si1.56)H1.0 has beenmeasured by Fujieda et al [117], see the end of section 7.1 for more details and a comparisonwith the alloy of the same La : Fe : Si ratios but without any hydrogen.

7.6. Addition of interstitial elements—carbon

Chen et al studied the effect of C additions to La(Fe11.6Si1.4)Cy [161] and to La(Fe11.5Si1.5)Cy

[163]. In both cases, carbon increased TC by about the same amount for the same y value,


from 195 K for y = 0 to 250 K for y = 0.6, but �SM was lowered—somewhat for low valuesof y (�0.2) and then much more rapidly for y � 0.4—e.g. for the LaFe11.5Si1.5Cy alloysit dropped from ∼−178 mJ cm−3 K−1 for y = 0 to −165 mJ cm−3 K−1 at y = 0.2 and to−91mJ cm−3 K−1 at y = 0.5. This rapid drop in �SM for y � 0.4 occurs because thefirst-order IEM transition changes to a second-order transition.

7.7. Direct measurement of MCE

The adiabatic temperature rise has been measured directly for three alloys of theLa(Fe13−xSix)Hy series. Hu et al [162] reported a �Tad value of 4 K for a 0 to 14 kOefield increase at 183 K for La(Fe11.7Si1.3). Assuming a linear magnetic field dependence weestimate a �Tad value of 5.7 K for a 0 to 20 kOe field change, which is probably a little highby 0.2–0.5 K. But since they did not make calorimetric measurements, this value cannot becompared with an indirect value obtained on the same sample. However, Fujita et al [141]reported an indirect �Tad = 8.1 K for a 0 to 20 kOe field change for an alloy of the samecomposition and TC = 184 K—a difference of 30%. But since the measurements were madeon two different samples, some variation might be expected, but not 30%. Fujieda et al [172]also made both indirect and direct �Tad measurements on the same sample, La(Fe11.44Si1.56).The directly measured �Tad value was 6 K at TC = 188 K for a 0–20 kOe field change, whichcompared with a calculated value of 7.6 K as determined from heat capacity measurement as afunction of temperature and magnetic field—a discrepancy of ∼20%. Fujieda et al [172] alsomeasured �Tad for La(Fe11.44Si1.56)H1.6 and reported a measured value of 4 K for a 0–20 kOefield change at TC = 319 K which is probably lower than the indirect value by 2 to 3 K, basedon his indirect values for samples with a similar Fe : Si ratio and similar hydrogen dopinglevels—a discrepancy of 50–75%. This topic is further addressed in section 10.1.

7.8. La(Fe13−xAlx)-based alloys

Not nearly as much work has been done on the Al-substituted alloys as for the Si-substitutedones, primarily because the MCE is rather modest. Hu et al [178] reported thatLa(Fe11.375Al1.625) exhibited two magnetic transitions, TN = 181 K (a second-orderparamagnetic to antiferromagnetic transition) and TC = 140 K (a first-order antiferromagneticto ferromagnetic transition). The MCE exhibits two peaks, a sharp one at 140 K and a broad oneat 180 K. The upper peak is quite small at low-magnetic fields, but becomes more pronouncedas the magnetic field increases, especially for H > 20 kOe, and it exceeds the first-orderpeak by 20% at 50 kOe (�SM for a 0–50 kOe field change is −44 mJ cm−3 K−1 at 140 Kand −54 mJ cm−3 K−1 at 181 K). In a second paper, Hu et al [53] reported that this alloyhas the cubic NaZn13-type structure from room temperature down to ∼10 K, but there is alarge lattice parameter discontinuity at ∼140 K which is consistent with the first-order natureof the transition at this temperature. The authors [178] reported there is a 5 K hysteresisassociated with this transition. Since the two ordering peaks are only 40 K apart, the MCEhas a table-like characteristic making it a candidate magnetic refrigerant for the Ericssoncycle [53]. The authors also note that even in a small field there is a large change in �SM,i.e. �SM = −22 mJ cm−3 K−1 for �H = 5 kOe.

Hu et al [155] also studied the MCE behaviour of La(Fe11.47Co0.23Al1.3) and noted thatthis small amount of Co is sufficient to change La(Fe11.7Al1.3) from an antiferromagnet to aferromagnet with TC = 198 K. The �SM value for �H = 50 kOe is −10.6 J kg−1K−1 (i.e.∼−74 mJ cm−3 K−1—the exact volumetric value cannot be determined because neither thelattice parameter nor the density were given), which is quite a bit smaller than the GMCE values


reported for the La(Fe13−xSix) and Gd5(Si4−xGex) alloys (∼−160 to ∼−200 mJ cm−3 K−1)

which have comparable TC values.Liu et al [179] reported the variation of the lattice parameters, magnetization, Curie

temperature and MCE (�SM) for the LaFe11(Si2−zAlz) pseudo-binary system. As might beexpected from the values of the two end members, TC and �SM both decrease as Si is replacedby Al, while the lattice parameter increases.

8. Manganites

The rare-earth manganites have been known for over 50 years [180], but their interestingmagnetocaloric properties were not reported until 1996 [7]. Since then, their MCEs have beenheavily studied, but to date the highest reported values are reasonable, but not outstanding likethose reported for several families of compounds discussed in the previous sections (4.1.1, 5,6.1, 6.2, 6.3 and 7). As a matter of fact several of the manganites have �SM values comparablewith Gd, but most are smaller.

Another major problem is that the MCE values reported by different groups generally varyquite widely (factors of 2 are not uncommon, and factors as much as 7 can be found amongthe data reported in the literature). Part of this difficulty is that the phase diagrams are verycomplex [180], and slight changes in the chemical compositions including oxygen deficienciescould easily account for differences in behaviour and in the reported values. Also heatingand processing variables can contribute to this problem. This is evident when one examinesfigure 10, where �SM is plotted against TC for a magnetic field change of 0–10 kOe. As onecan see, there is no correlation, not like what is observed for other families of compounds, seefigure 3.

The preparation of the manganites is generally quite involved, regardless of the methodused: mixing of the solid components, a sol–gel process or an aqueous process. After theinitial mixing of the starting ingredients by one of these three methods, the mixture is heatedto between 800˚C and 1200˚C for 10–24 h, cooled, reground, reheated, cooled, ground oncemore and then sintered into pellets.

8.1. (La1−xMx)MnO3 where M = Na and Ag

Chen et al [181] measured the change in the MCE of rhombohedral (La0.8Na0.2)MnO3−δ asa function of the oxygen deficiency, δ, up to δ = 0.07. They found that the maximum �SM

value (�SM = −23.2 mJ cm−3 K−1 for �H = 10 kOe at 364 K) occurs for δ = 0.06, whichis one of the highest �SM values reported for a manganite phase, see figure 10, point 2. Butwhen compared with other materials, see figure 3, the �SM value is quite small. This phasealso has one of the highest Curie temperatures for manganite materials.

The MCE of some rhombohedral (La1−xAgx)MnO3 phases was reported by Tang et al[182] for x = 0.05, 0.20, 0.25 and 0.30 and by Wang et al [183] for x = 0.22. The compoundsfor x = 0.05, 0.25 and 0.30 exhibit an SOMT and the �SM value is quite small (∼one half)compared with that for x = 0.20 (�SM = −22.8 mJ cm−3K−1), which undergoes an FOMTat 278 K [182]. This value is somewhat larger than that reported for (La0.78Ag0.22)MnO3

at TC = 301 K(−18.2 mJ cm−3K−1). Both values are for �H = 10 kOe and are shown infigure 10, points 3 and 4, respectively.

8.2. (La1−xCax)MnO3

8.2.1. La deficiency. The MCE of the (La1−xCax)MnO3 phases has been extensively studied,probably the most thoroughly investigated manganite family. Chen et al [184] have studied the


Figure 10. The magnetocaloric entropy change for �H = 10 kOe of the lanthanide manganitesversus the Curie temperature. A magnetic field change of 0–10 kOe was used, since a majorfraction of the manganites were studied at low-magnetic fields, <30 kOe. The most commonfield change was for 0–10 kOe, while �SM values measured in 50 kOe were rare. The valuefor (La0.835Na0.165)MnO3, point 1, was taken from [7], the remaining values are taken from thereferences cited in section 8.

Compound legend1—(La0.835Na0.165)MnO3 [6.142] 7—(La0.60Ca0.40)MnO3 [5.705]2—(La0.8Na0.2)MnO2.94 [6.009] 8—(La0.60Ca0.40)MnO3 [5.683]3—(La0.8Ag0.2)MnO3 [6.699] 9—(La0.66Ca0.11Pb0.23)MnO3 [6.704]4—(La0.78Ag0.22)MnO3 [6.682] 10—(La0.65Sr0.35)MnO3 [6.4]5—(La0.77Ca0.20)MnO3 [5.938] 11—(Nd0.67Sr0.33)MnO3 [6.3]6—(La0.70Ca0.30)MnO3 [5.957] 12—(La0.67Ba0.33)MnO3 [6.797]

effect of La deficiencies on TC and the MCE of (La0.8−yCa0.2)MnO3 (density is 5.938 g cm−3).The Curie temperature rises from 182 K for no La deficiency to 260 K for y = 0.05, and thenTC tends to remain nearly constant or decrease slightly up to y = 0.10. As y increases, thenature of the magnetic transformation changes from SOMT (for y = 0 and 0.01) to FOMT (fory = 0.03 to 0.10), and the maximum value of the MCE increases from �SM = −7.7 at y = 0to �SM = −22.3 mJ cm−3K−1 at y = 0.03 for �H = 10 kOe (point 5 in figure 10). For0.05 � y � 0.10, �SM remains approximately constant at −16.0 mJ cm−3 K−1. Phan et al[185] also studied the influence of La deficiencies in single crystalline (La0.8−yCa0.2)MnO3

for y = 0.05 and 0.20. The results reported by the latter authors differ considerably fromChen et al’s results noted above. The TCs for y = 0.05 differ by nearly 100 K (170 Kfor Phan et al’s sample versus 260 K for Chen et al’s sample) and �SM is considerablysmaller when considering the difference in the magnetic field change of −18.5 mJ cm−3 K−1

(assuming a density of 5.94 g cm−3) for a �H = 50 kOe [185] versus −16.0 mJ cm−3 K−1

for �H = 10 kOe [184]. Phan et al reported that they observed spin glass behaviour in theirsample (y = 0.05) with TSG = 100 K, which may account for some of the differences in theproperties of the two (La0.75Ca0.2)MnO3 samples.

8.2.2. Unsubstituted La or Ca. Another study [55] of a single crystal, specifically(La0.7Ca0.3)MnO3 (density is 5.947 g cm−3), is consistent with the results noted in the previous


paragraph. Sun et al [186] report TC = 227 K and �SM = −11.6 mJ cm−3 K−1 for�H = 10 kOe (point 6 in figure 10) and −38.3 mJ cm−3 K−1 for �H = 50 kOe. Themore recent results reported by Phan et al [187] for both a single crystal and a polycrystallinesample of this composition are essentially identical to those reported by Sun et al .

Both Sun et al [186] and Xu et al [188] measured the MCE (�SM) for (La0.67Ca0.33)MnO3

(density is 5.947 g cm−3). The former gives �SM = −38.1 mJ cm−3 K−1 at TC = 267 Kfor a 0–30 kOe magnetic field change, while the latter reports −20 mJ cm−3 K−1 at TC =275 K for �H = 20 kOe. These results are in reasonable agreement with each otherconsidering the difference in the magnetic field change. The MCE properties of orthorhombic(La0.6Ca0.4)MnO3 were studied by Bohigas et al [189] and Dinesen et al [190] for several fieldchanges between �H = 5 kOe and �H = 30 kOe (by both groups). The lattice parameterswere given by both groups; in general those reported by Dinesen et al were larger by about0.01 A and thus the density was slightly smaller, 5.705 g cm−3 [189] versus 5.683 g cm−3

[190]. Also, TC was larger (268 K versus 260 K), but the MCE values for the correspondingfield changes were ∼15% smaller for the material of Dinesen et al. The �H = 10 kOe valuesare shown in figure 10, points 7 [189] and 8 [190]. The preparation techniques might accountfor these differences: Bohigas et al [189] used a solid state technique, while Dinesen et al[190] used an aqueous approach.

8.2.3. Substitution for La. The substitution of other lanthanides for La has been reportedby Wang et al [191] for Nd substitutions and by Chen et al [192] for Ce, Gd, Tb andDy substitutions. Wang et al studied (La0.7−yNdyCa0.3)MnO3 (density is 5.957 g cm−3

for y = 0) at doping levels of y = 0, 0.03, 0.10, 0.15 and 0.20. They found that�SM increased and TC decreased with increasing x. �SM for �H = 10 kOe rose from−8.2 mJ cm−3 K−1(TC = 256 K) at y = 0 to −13.9 mJ cm−3 K−1 (TC = 213 K) at y = 0.20.

In contrast to the continuous increase in �SM noted in the previous paragraph for(La0.7−yNdyCa0.3)MnO3, Chen et al [192] found the �SM value peaked at x = 0.1 for([La1−yRy]0.67Ca0.33)MnO3, where R = Ce, Gd, Tb and Dy. In most cases, dopingconcentration of y = 0, 0.1 and 0.3 were studied, except for Gd, where only y = 0.1was investigated. The base parameters (i.e. y = 0 (density is 5.947 g cm−3)) were:�SM = −22.9 mJ cm−3 K−1 at TC = 246 K for a �H = 15 kOe. The maximum �SM values(y = 0.1) for the same field change are: −27.0 mJ cm−3 K−1 for Ce; −34.8 mJ cm−3 K−1 forGd; −28.7 mJ cm−3 K−1 for Tb; and −36.8 mJ cm−3 K−1 for Dy. �SM appears to increasewith increasing atomic number, except for Tb. The depression of TC is greatest in Tb, followedby Dy, Gd and Ce in decreasing effectiveness.

8.2.4. Substitution for Ca. Sr and Pb substitutions for Ca in (La1−xCax)MnO3 havebeen reported by Zhang et al [193] and Sun et al [194], respectively. Zhang et al studiedorthorhombic (La0.75[Ca1−ySry]0.25)MnO3 (density is 6.21 g/cm−1 for y = 0.075) fory = 0.075 and 0.10. For y = 0.075 the MCE values for a 0–14 kOe field change are�Tad = 0.78 and �SM = −16.7 mJ cm−3 K−1 at TC = 295 K. With additional Sr (y = 0.10),the peak at TC changes from a sharp peak to a broad flat maximum between 285 and 315 K,with �Tad = 0.49 K; no �SM value was reported for this composition.

Sun et al [194] studied an orthorhombic (La0.66Ca0.11Pb0.23)MnO3 single crystal whichhad been grown from a PbF2/PbO flux. The MCE was determined for four field changes,�H = 10, 20, 40 and 70 kOe. The �SM value for �H = 10 kOe is −14.1 mJ cm−3 K−1,point 9 in figure 10. They concluded that the manganites do not seem to be promising candidatesfor magnetic refrigeration.


8.3. (R1−xSrx)MnO3

8.3.1. (La1−xSrx)MnO3. Demin and Koroleva [195] investigated �Tad for a series of singlecrystal (La1−xSrx)MnO3 compounds, where 0.1 � x � 0.3, and found that both �Tad

and TC increased with an increased Sr level. The �Tad values for �H = 8.2 kOe and TC

values are: 0.2 K at 175 K for x = 0.1; 0.37 K at 180 K for x = 0.125; 0.7 K at 260 K forx = 0.175; and 0.78 K at 346 K for x = 0.3. Szewczyk et al [196] measured the MCEproperties of (La0.845Sr0.155)MnO3 (the density is ∼6.3 g cm−3) for a field change of 70 kOe.They report �Tad = 3.3 K as measured directly, and 3.5 as calculated from the heat capacityat TC = 234 K; and �SM = −42 mJ cm−3 K−1.

Xu et al [188] reported that �SM = −1.7 mJ cm−3 K−1 at TC = 368 K for �H = 0.5 kOefor (La0.67Sr0.33)MnO3 (density is 6.230 g cm−3). The MCE of (La0.65Sr0.35)MnO3 (densityis ∼6.4 g cm3) was investigated by Phan et al [197]. They report �SM = −13.6 mJ cm−3 K−1

for a field change of 10 kOe (point 10 in figure 10) and TC = 305 K.

8.3.2. Substitution for Sr or Mn. Phan et al [197] studied the effect of substituting Ca andBa for Sr. For (La0.6Sr0.2Ca0.,2)MnO3 (density is ∼6.3 g cm−3) they reported TC = 337 Kand �SM = −12.3 mJ cm−3 K−1 for �H = 10 kOe, and for (La0.6Sr0.2Ba0.2)MnO3 with adensity of ∼6.5 g cm−3 they give TC = 354 K and �SM = −14.7 mJ cm−3 K−1 for the samefield change. It is difficult to state whether the Ca or Ba substitutions are beneficial or notsince the unsubstituted compound had a different La to Sr ratio, i.e. (La0.65Sr0.35)MnO3 (seeprevious paragraph). Considering that the �SM values are for �H = 10 kOe and the highTC values, these two compounds are potential candidate active magnetic regenerator materialsabove room temperature, especially (La0.6Sr0.2Ba0.2)MnO3.

Chau et al [198], on the other hand, substituted Cu for Mn in the compound(La0.7Sr0.3)(Mn1−zCuz)O3, where z = 0.05 and 0.10 (the densities are 6.311 and 6.298 g cm3,respectively). The TC value was the same for both values of z, 350 K, while �SM =−12.4 mJ cm−3 K−1 for z = 0.05 and −13.0 mJ cm−3 K−1 for = 0.10 for a field change of12.5 kOe. Again no information was given for the unsubstituted compound and so comparisonsand/or trends cannot be made or established.

8.3.3. (Nd0.67Sr0.33)MnO3. Si et al [199] measured the MCE in (Nd0.67Sr0.33)MnO3 (densityis ∼6.3 g cm−3) for field changes of 10, 15, 20, 30 and 50 kOe. For �H = 10 kOe,�SM = −20 mJ cm−3 K−1 at TC = 257.5 K, point 11 in figure 10. The �H = 50 kOevalue of �SM is −47 mJ cm−3 K−1, which falls close to the SOMT line in figure 3.

8.4. Charge Order

In some of the (R1−xSrx)MnO3 compounds when the FM-metallic state transforms to a lowtemperature AFM-insulator state a spatial ordering of the Mn3+ and Mn4+ ions occurs. Thisfirst-order transition is known as a charge order transition, with a characteristic temperatureTCO. At TCO, there is a sudden large change in the lattice parameters (usually a and b increaseand c decreases), but the unit cell volume hardly changes [200]. Magnetic fields have a largeinfluence on TCO, i.e. a 50 kOe field change lowers TCO by ∼40 K and induces a large negativeMCE (i.e. a positive �SM). There is also a large hysteresis associated with the influence ofthe magnetic field on the charge ordering, i.e. ∼10 kOe and ∼10 K near TCO.

8.4.1. (Pr1−xSrx)MnO3. Chen et al [201] studied the (P r1−xSrx)MnO3 system at threedifferent compositions, x = 0.3, 0.4 and 0.5. As x increases, TC was lowered from 260 K


(x = 0.3) to 243 K (x = 0.4) to 205 K (x = 0.5), and the �SM for �H = 10 kOe increasedfrom −11.6 to −13.1 to −17.5 mJ cm−3 K−1 for the respective x values. Of these threecompositions, only the (Pr0.5Sr0.5)MnO3 phase (density is 6.650 g cm−3) exhibited chargeordering at TCO = 161 K and �SM = +47.2 mJ cm−3 K−1 for �H = 10 kOe. Chen andDu [202] found that when Nd is substituted for Pr in ([Pr1−yNdy]0.5Sr0.5)MnO3 (y = 0,0.3, 0.5, 0.7 and 1.0), TC and TCO are increased from 205 to 267 K for TC and from 161 to183 K for TCO, but �SM seems to be approximately constant (∼47.5 ± 5.0 mJ cm−3 K−1) fora change of 10 kOe for the five samples, varying from +43.2 mJ cm−3 K−1 for y = 0.7 to+52.5 mJ cm−3 K−1 for y = 0.5, with the other three values falling between these two limits.Also see section 8.4.2.

Reis et al [203, 204] found that charge ordering co-exists with an AFM insulator state for0.30 � x � 0.85 in the (Pr1−xCax)MnO3 system (density is ∼5.1 g cm−3 for x = 0.32). Inthe composition region 0.30 � x � 0.40 the CO/AFM-insulator phase transforms at ∼50 Kto the CO/FM-insulator phase. At ∼25 K, the charge ordered state is completely melted if theapplied magnetic field is large enough and an insulator to metal transition is induced, leadingto a large �SM value. For x = 0.32 and �H = 40 kOe, �SM = −106 mJ cm−3 K−1. This�SM value falls well below the SOMT dashed line shown in figure 3. Gomes et al [205] reportthat Gd, when substituted for Pr (i.e. (Pr0.43Gd0.25Sr0.32)MnO3), drastically lowers the �SM

value of the undoped (Pr0.68Sr0.32)MnO3 material.

8.4.2. (Nd1−xSrx)MnO3. The MCE in the charge order compound (Nd0.5Sr0.5)MnO3 (thedensity is 6.405 g cm3) has been studied by three groups of investigators, Chen and Du [202](also see section 8.4.1), Sande et al [206] and Chau et al [207]. The reported values forTC, TCO and �SM vary widely. Chen and Du give the following values: TC = 268 K,TCO = 183 K and �SM = +48.5 mJ cm−3 K−1 at TCO for �H = 10 kOe. Sande et alfound TC = 240 K, TCO = 155 K and �SM = +17.9 mJ cm−3 K−1 at TCO for �H = 10 kOe.The latter also give �SM = −5.8 mJ cm−3 K−1 at TC for �H = 10 kOe. Chau et al reportTC = 265 K, TCO = 175 and �SM = +8.6 mJ cm−3 K−1 at TCO for �H = 10 kOe. Similarly,when the results reported by Chau et al [207] are compared with those of Chen and Du [202] for(Nd0.25Pr0.25Sr0.5)MnO3, there are again some significant differences. For this alloy, Chen andDu give TC = 225 K, TCO = 168 K and �SM = +52.5 mJ cm−3 K−1 at TCO for �H = 10 kOe,while Chau et al report TC = 265 K, TCO = 170 K and �SM = + 7.3 mJ cm−3 K−1 at TCO for�H = 10 kOe. There are no obvious reasons for these large discrepancies, but as noted in theintroductory paragraphs of this section (8), the manganite phase diagrams are quite complex,and slight variations from the assumed, nominal compositions might account for the variationsin the reported results.

Chau et al [207] examined the effect of substituting Cu for Mn on the charge orderingbehaviour in (Nd0.5Sr0.5)(Mn1−yCuy)O3. When y = 0.02, TC is lowered from 265 K (fory = 0) to 230 K and TCO is lowered from 175 to 170 K; and when y = 0.10, charge orderingis destroyed and TC rises back up from 230 K at y = 0.02 to 260 K. Presumably the �SM

value at TCO is lowered for y = 0.02, since charge ordering is destroyed when additional Cu(y > 0.02) is substituted for Mn.

8.5. (La1−xBax)MnO3

The MCE properties of (La0.67Ba0.33)MnO3 have been reported by Xu et al [188] and Zhonget al [208]. The former found TC = 345 K and �SM = −0.8 mJ cm−3 K−1 for a fieldchange of 0.5 kOe, while the latter stated that at TC = 337 K, �SM = −18.8 mJ cm−3 K−1

for �H = 10 kOe (point 12 in figure 10). As one can see, the TCs are in fair agreement and


the �SM values are probably in agreement, considering the differences in the magnetic fieldchanges.

Zhong et al [208] also studied the effect of oxygen deficiencies in (La0.67Ba0.33)MnO3−z.Five compositions were studied: z = 0, 0.02, 0.05, 0.08 and 0.10. Both TC and �SM decreasenearly linearly with increasing z: TC is lowered from 337 K for z = 0 to 268 K for z = 0.10,and �SM for �H = 10 kOe is lowered from −18.8 to −12.0 mJ cm−3 K−1 for the same z

values.The compound (La0.70Ba0.24Ca0.06)MnO3 (density is 6.46 g cm3)was investigated by Phan

et al [197], who found TC = 320 K and �SM = −11 mJ cm−3 K−1 for �H = 10 kOe. Sinceno baseline composition was studied, the influence of Ca substitution for Ba is not known.

8.6. (La1−xMx)3Mn2O7

The (La1−xMx)3Mn2O7 phases crystallize in the Sr3Ti2O7-type structure. Zhu et al [209]studied the MCE properties of (La1.4Ca1.6)Mn2O7 at 20 and 50 kOe. They report that�SM at TC = 270 K for �H = 20 kOe is −62.6 mJ −3 K−1, and for �H = 50 kOe it is−93.0 mJ cm−3 K−1. This latter value lies above the SOMT line in figure 3 (point 44), closeto the Gd point (17), and thus might make a reasonably good AMR refrigerant.

Zhong et al [210] measured the MCE properties of a series of (La2.5−xK0.5+x)Mn2O7,where x = 0.05, 0.15, 0.25, 0.35 and 0.45. They found that with increasing x, TC increasedin a nearly linear fashion from 200 K (x = 0.05) to 254 K (x = 0.45), while the �SM

value for �H = 10 kOe increased from −4.1 mJ cm−3 K−1 at x = 0.05 to a maximum of−8.3 mJ cm−3 K−1 at x = 0.35 and then the �SM value decreased to −6.2 mJ cm−3 K−1 atx = 0.45.

9. Nanocomposites

As a bulk magneto-thermal property, the MCE of nanocomposites, in general, is expectedto be quite low because magnetocaloric nanoparticles must be dispersed in a matrix so as toprevent their agglomeration associated with the minimization of surface energy. The matrixusually shows little if any magnetocaloric activity in the same temperature range as theactive magnetocaloric nanoparticles do. Furthermore, in a typical nanocomposite material,the concentration of nanoparticles usually remains below 50% by volume. Thus, the extensivemeasure of the MCE is reduced by a factor proportional to the ratio of the volumes (orthe masses) of the inactive matrix and the active particulate, while the resultant intensiveMCE is suppressed because the matrix acts as a high-capacity heat sink. Matrix effectsaside, nanoparticles, which usually show superparamagnetic behaviour, have been knownto exhibit enhancement of the MCE when compared with conventional paramagnets. It is,therefore, feasible that basic research on the MCE of nanocomposites will lead to a betterunderstanding of the relationships between the structure, magnetism and thermodynamics ofsolids. These materials may also find future applications in low-temperature (below 20 K)magnetic refrigeration devices, especially because high surface areas intrinsic to nanoparticlescould result in improvements of the heat transfer. However, use of nanocomposites in practicalnear room temperature magnetic refrigerators remains problematic for the foreseeable future.

In recent years, only a few reports about the MCE of nanocomposites have been published.Thus, Yamamoto et al [211] and [212] investigated Fe2O3–Ag nanocomposites containing9 at% and 40 at% of iron oxide particulate ranging in size from 10 to 35 nm. In the lowiron content material, iron oxide was in the form of γ -Fe2O3, while in the high iron contentmaterial, the formation of α-Fe2O3 has been detected. The isothermal magnetic entropy


change around 250 K in the 9% Fe and 40% Fe samples reached ∼2.1×10−3 J mol−1(Fe) and∼1.5 × 10−3 J mol−1(Fe), respectively, in magnetic fields varying from 0 to 7 T (because ofthe lack of information about the densities, the values were not converted into mJ cm−3 K−1

units). Despite the very small absolute �SM values, they exceed those of normal paramagneticFe3+ in the same temperature and magnetic field range by about two orders of magnitude.This enhancement has been attributed to the superparamagnetic behaviour of iron oxidenanoparticles. The same authors [212] examined the MCE of iron nitride nanoparticles,also embedded into a silver matrix. Two different iron nitrides (γ ′-Fe4N and ε-Fe3N) wereobserved in a 6 at% Fe–Ag nanocomposite. Iron nitride nanoparticles exhibited a factor of2–3 enhancement of the MCE when compared with the 9% Fe–Ag nanocomposite. Thisimprovement has been associated with the two-component effect: one was due to preferredorientation of the effective magnetic moments of nanograins and the other was due to thetemperature dependence of the ferromagnetic coupling strength between electrons in theε-Fe3N phase.

It is well established [213] that nanostructuring may lead to a nanoparticle exhibiting aneffective magnetic moment which is greater than the magnetic moments of the constituentatoms. Thus, Yamamoto et al [214] examined how the magnitude of the effective magneticmoment influences the resulting MCE of 12 at% Fe to 33 at% Fe iron oxide nanoparticlesranging in size from 10 to 30 nm which were embedded in a silver matrix. They concludedthat for a maximum enhancement of the MCE, it is desirable to have as uniform distributionas possible of particle sizes because the latter controls their effective magnetic moments.This hypothesis was later confirmed experimentally by Kinoshita et al [215], who examinedmagnetite—Au nanocomposites with a narrow size distribution of Fe3O4 particles rangingfrom 4.6 to 7.4 nm in diameter. The measured �SM value was several times greater whencompared with iron oxide–Ag composites with 10–30 nm size variance.

In addition to iron-based nanocomposites, a few materials containing rare-earth elementshave been examined with respect to their magnetocaloric properties. Thus, Provenzano et al[216] report that heat treatment has a considerable effect on the MCE of R3Ga5−xFexO12

materials with R = Gd, Dy and Ho and x ranging from 0 to 5. These garnets arenanocomposites, in which clusters of iron atoms naturally form during the material’s synthesis.It was established that �SM decreases from R = Gd to Ho and Dy despite the fact that the totalangular momentum decreases in the series Ho–Dy–Gd. This counterintuitive observation wasexplained by a reduction of the interaction strength between the rare-earth elements and theFe as the Gd is replaced by Dy and Ho and the fact that Dy reduces this interaction strengthfaster than does Ho. The largest MCE (�SM ∼= −1.7 J kg−1 K−1, which corresponds to∼12 mJ cm−3 K−1 assuming that the density of this iron-substituted garnet is ∼7 g cm−3) wasobserved around 10 K in Gd3Ga2.5Fe2.5O12 for a magnetic field change of 10 kOe. Provenzanoet al [217] also studied Gd60Al28Fe12 and Gd45Al33Fe22 alloys, where the addition of Gdto Fe–Al alloys ‘was expected to form magnetic clusters with much larger moment of theGd atom’. The alloy chemistries were based on the binary Gd3Al2 intermetallic compound,earlier studied by Pecharsky et al [218], and the non-existent ‘Gd4Al5’ compound, respectively.Addition of Fe to the Gd3Al2 lowers the two MCE maxima from 49 and 282 K to ∼10 and ∼50 K, respectively; the �SM value of the lower temperature peak is increased by about a factorof 3, but the MCE of the high-temperature peak is lowered by approximately the same factorwhen compared with Gd3Al2. Nelson et al [219] attempted to prepare nanoparticles of Gd insolution, yet they had considerable difficulties in preventing particle oxidation. The majorityof particles were 10–15 nm in diameter and their MCE is essentially zero at all temperaturesabove ∼100 K (bulk Gd is one of the best known MCE materials, with the MCE exhibiting apeak around 294 K, see figure 3, point 17). The MCE of these ‘Gd ’ nanoparticles increases as


temperature decreases, as one would expect for a normal Curie-type paramagnet. It is worthnoting that theoretical predictions by Shir et al [220] indicate that Gd nanoclusters may have asubstantial MCE at the same temperature as bulk Gd metal does. Unfortunately, this theoreticalresult clearly disagrees with the earlier experiments [219], yet Shir et al [220] give no detailson how to bring the Curie temperature of Gd nanoclusters all the way to room temperature.

10. Correlations

10.1. Adiabatic temperature rise: direct versus indirect measurements

As noted by Gschneidner and Pecharsky [7], an FOMT presents some special problems whendetermining �Tad by either direct or indirect methods. These authors noted that the kinetics ofthe first-order transformation may be slow and the rapid magnetic field change required to fulfiladiabatic conditions may not be slow enough to allow the transformation to go to completion.And if the thermal isolation of the sample is not good enough, the directly measured �Tad

value can be underestimated.The authors [7] also pointed out that the �Tad value obtained from indirect measurements

can also be in error, although the kinetics may not be a limiting condition since the experimentaldata are taken under quasi-equilibrium conditions. The major problem may occur whenapplying the Maxwell equations (3) and (4) at the FOMT, especially if it is a sharp first-order transition. In practice, for the majority of materials the transitions are not ideal (i.e. nottruly discontinuous) and thus one can calculate the derivative ∂M(T , B)/∂T and it is possibleto use the Maxwell equations. For more details the reader is referred to [19, 221].

As mentioned earlier in this review, there are some discrepancies between the direct �Tad

measurements and the �Tad values determined from heat capacity measurements for bothGd5(Si2Ge2), see section 5.2, and La(Fe13−2Six), see section 7.7. The direct measurement of�Tad for a material which exhibits an FOMT needs to be carried out under nearly equilibriumconditions, i.e. the field change needs to be sufficiently slow to enable the completion ofthe phase transition, much slower than is used normally [109]. For Gd5(Si2Ge2) the normalprocedure leads to a too small a value by ∼50% for �Tad (i.e. 8.5 K) [108] compared withthe indirect value obtained from heat capacity measurements (16.5 K) [109], while the �Tad

value determined by slowly ramping the field up or down agrees with the indirect value within±5% [109]. For La(Fe13−xSix) base materials, the direct and indirect �Tad values are availablefor two different alloy compositions. The direct �Tad value of 5.7 K for La(Fe11.7Si1.3) (seesection 7.7) is ∼30% smaller than the indirect value of 8.1 K [141], and for La(Fe11.44Si1.56)�Tad (direct) = 6 K is ∼20% smaller than �Tad (indirect) = 7.6 K [172]. These resultssuggest that there may be a time dependence of the �Tad measurement for an FOMT, whichprobably varies from one material to another.

For SOMT materials, the direct and indirect �Tad values are generally in good to excellentagreement, even when pulse field techniques are used to measure �Tad [54, 222]. For the sameGd sample the pulse field �Tad value was in agreement with the calorimetric value within∼2%, and for different Gd samples the two �Tads agree within ±5% [54, 222]. However, forone sample which had a high C content, the dynamic pulse field values were ∼50% smallerthan the calorimetric �Tad value [54].

The difference between the SOMT and FOMT is that it is only the spin system respondingto the magnetic field change during SOMT, but for FOMT materials, both the magnetic andcrystal sublattices couple to the external magnetic field and, as a result, atoms are displacedduring the transformation. In the former case, the response time is in nanoseconds, while forthe latter it can be many orders of magnitude longer.


It should be noted that these values are based on static (heat capacity) and semi-static(magnetization and direct), i.e. equilibrium or near-equilibrium, measurements. But in mostmagnetic refrigerators the magnetization and demagnetization steps are dynamic, and in somecases may become non-equilibrium processes, i.e. the devices run at from 0.1 to 4 Hz and thusthe direct measurements of �Tad may closer approximate the actual conditions experiencedin a magnetic refrigerator than the static values of �Tad determined from heat capacitymeasurements.

10.2. The lattice entropy

A recent study of a magnetic field induced structural transformation (FIST) in Gd5Ge4 hasled to a better understanding of the GMCE [223]. This transformation, which occurs below30 K, was studied by powder x-ray diffraction in magnetic fields of up to 35 kOe in addition tomagnetization and heat capacity measurements. The results demonstrated that GMCE arisesfrom the amplification of the conventional magnetic entropy change by the entropy differencebetween the two structures: the low-temperature (high-magnetic field) ferromagnetic Gd5Si4-type structure and the high-temperature (low-magnetic field) antiferromagnetic Sm5Ge4-typestructure. For a FIST the total measured entropy, �ST, can be partitioned into two components,�SM and �Sst, where �SM is given by equation (3) and �Sst is the entropy difference betweenthe two crystallographic modifications. Unfortunately, when the magnetic and structuraltransitions are coupled, one can only measure the total entropy change, �ST, and this iswhy �Sst has been called a ‘hidden parameter’ [223]. However, the authors estimated thatat low-magnetic fields (<20 kOe) �Sst could account for about half of �ST. In a morerecent paper [224] these authors were able to quantify �Sst by considering the �ST forGd5(Si2Ge2), which orders at 270 K, undergoing a coupled magnetic/structural transformationexhibiting the GMCE, and the �SM for Gd5(Si2.5Ge1.5), which orders at 312 K, undergoinga pure magnetic transformation (i.e. a SOMT). Since the former transforms structurally froma monoclinic Gd5Si2Ge2 modification to the orthorhombic Gd5Si4 structure, and the lattermaintains the orthorhombic Gd5Si4 structure in both the paramagnetic and ferromagneticstates, the differences between �ST[Gd5(Si2Ge2)] and �SM = �ST[Gd5(Si2.5Ge1.5)] give�Sst for the monoclinic ↔ orthorhombic structures. From the difference in the MCE peakvalues of the respective �ST versus T plots, they obtained a value of 74 ± 3 mJ cm−3 K−1

(1.08 ± 0.04 J g at−1 K−1) for �Sst. The authors point out that �Sst is of the same order ofmagnitude as the entropies of transformation of the pure metals.

In the case of Tb5(Si2Ge2), Morellon et al [225] showed that the magnetic and structuraltransformations are decoupled at atmospheric pressure: the former takes place at TC = 111 Kand the latter occurs at Tst = 93 K. When hydrostatic pressure is applied, both TC andTst increase, but the structural transformation temperature rises more rapidly, such that theymerge (TC = Tst ∼= 115 K) at 8.6 kbar. From the pressure dependence of the MCE, Morelonet al estimate a �Sst of not less than 70 mJ cm−3 K (1.0 J g at−1 K−1), which is in excellentagreement with that of Gd5(Si2Ge2), especially considering the difference in the orderingtemperatures of the two materials. The nearly ideal match of the �Sst of Tb5(Si2Ge2) withthat of Gd5(Si2Ge2), determined using two different approaches, reflects the fact that both thelow-field (monoclinic paramagnetic state) and high-field (orthorhombic ferromagnetic state)crystal structures of the two compounds are the same.

For those materials which exhibit an FOMT due to IEM, there is also a hidden entropychange associated with the large volume (or lattice parameter) change that occurs whenthe material undergoes the magnetic transition, i.e. �SIEM. Since most of these materials[La(Fe13−xSix) and MnFe(P1−xAsx)] will change from an FOMT to an SOMT upon alloying,


it is possible that one can estimate �SIEM in a manner similar to the way �Sst was determinedfor the Gd5(Si1−xGex)4 alloys. As far as we are aware this has not been done.

10.3. The magnetic field dependence of the MCE

The isothermal entropy change as a function of the applied magnetic field for a select number ofkey magnetocaloric materials is shown in figure 2(a). It is noted that the materials that exhibit anFOMT [MnAs, La(Fe11.44Si1.56), DyCo2 and Gd5(Si2Ge2)] show a rapid rise at low-magneticfields as compared with the materials which have an SOMT [Gd, La(Fe11.375Al1.625) and(La0.7Ca0.3)MnO3]. This enhancement is due to the �Sst or �SIEM contributions (see section10.2) which are field independent as long as the magnetic field is sufficiently high to induce andcomplete an FOMT. This is also consistent with the almost uniform slopes of �SM versus H

above H = 20 kOe. These data suggest that |�Sst(MnAs)| > |�Sst(Gd5Si2Ge2)|, while the�SIEM values of La(Fe11.44Si1.56) and DyCo2 are comparable and, perhaps, somewhat greaterthan the |�Sst(Gd5Si2Ge2)|.

The comparable plot of the adiabatic temperature rise versus H for �H � 20 kOe(figure 2(b)) shows that all of the materials have about the same initial slope regardless ofthe order of the magnetic transition. For H > 20 kOe the two materials which exhibitFOMT due to IEM [La(Fe11.44Si1.56) and DyCo2] have considerably smaller slopes thaneither Gd or the two materials which exhibit a coupled structural/magnetic FOMT [MnAs andGd5(Si2Ge2)].

Furthermore, these two plots, figures 2(a) and (b), show that just because a materialexhibits a large �SM value, �Tad will not also be large. This is especially true for the twomaterials which exhibit an FOMT due to IEM, La(Fe11.44Si1.56) and DyCo2, which exhibitthe opposite behaviour—a large �SM value (figure 2(a) and a relatively small �Tad value(figure 2(b)).

10.4. The temperature dependence of the MCE

10.4.1. The magnetic entropy change, �SM. Several years ago it was pointed out that thelattice heat capacity, CL, could account for the variation in �SM values for the RAl2 phases andfor the difference in �SM for GdPd and (Dy0.5Er0.5)Al2, both of which order at ∼40 K [226].The authors noted that the larger CL, the smaller �SM. This is due to the fact that a high CL valueincreases the thermal load and more energy is required to heat the sample itself, i.e. there is anentropy loss. The reduction of �SM is expected to be the largest at high temperatures, above50–100 K, since CL is inversely proportional to the Debye temperature, D, see figure 11. Withthis in mind we now examine the temperature dependence of the magnetic entropy change fora 0 to 50 kOe field change for many of the ferromagnetic materials, which is shown in figure 3.Except for the Mn(As1−xSbx) family of alloys, �SM tends to rise as T decreases, regardless ofthe order of the transformation. At high temperatures, over 150 K, �SM is nearly independentof temperature for the SOMT materials (figure 3), which is consistent with the nearly saturatedCL for T � 150 K (figure 11). For the FOMT RCo2, Gd5(Si1−xGex)4 and MnFe(P1−xAsx)families of alloys, �SM also decreases with increasing temperature.

It is seen that the Mn(As1−xSbx) family of compounds shows a different trend: even ifwe exclude the �SM values below ∼240 K, the �SM values slightly increase with increasingtemperature. This behaviour, however, is consistent with the trend noted above (when CL islarge �SM is small) because Sb has a lower D than does As [227], and thus Sb has a higherCL than does As at T < 300 K (see figure 11), and when Sb is substituted for As, both �SM

and TC become smaller, see figure 6.


Figure 11. The dimensionless lattice heat capacity of three solids with different Debyetemperatures, D, versus temperature. Most of the materials discussed in this review have D

values between 150 and 350 K.

The rapid drop in �SM for the Mn(As1−xSbx) and MnFe(P1−xAsx) families near the low-temperature terminus of the �SM versus T curves for these two families is unusual. For theformer family, the FOMT changes to SOMT for T ∼= 250 K, and �Sst = 0 for the highSb alloys (x > 0.3). However, for the MnFe(P1−xAsx) family, all the alloys are FOMTmaterials, and thus the drop-off cannot be due to a change in the order of the transformation,but it might be due to a decrease of IEM energetics which leads to a reduction in �SM but nota change in the order of the transformation. Another possible explanation for this drop-off atlarge P concentrations (x < 0.35) may be due to the stronger antiferromagnetic exchangeand subsequent reduction in the Mn magnetic moments.

10.4.2. The adiabatic temperature rise, �Tad. More recently it was shown in athermodynamic analysis of the MCE that �Tad is proportional to T/C and that for the same�SM, �Tad is expected to be large as the T increases and/or C decreases [170]. Since C goesmore rapidly to zero than T , T/C becomes quite large and �Tad is expected to be large asT approaches 0 K (we note that at T = 0 K, both the magnetic entropy change and adiabatictemperature change are also zero). At high T , i.e. >200 K, C approaches the DuLong–Petitlimit and �Tad will increase with increasing temperature for the same �SM. Since C ∼= CL,except for T < 10 K, C will have a temperature dependence similar to that shown in figure 11,and T/C will have a minimum between ∼50 and ∼100 K, and thus �Tad will also have aminimum in the same temperature range. Of course the temperature of the T/C minimumdepends on D of the solid (see figure 11).

We now examine figure 4 which is a plot of �Tad versus T for �H = 20 kOe and for�H = 50 kOe. One can see that there is a trend of the data to be large for T < 25 K, reacha minimum between 50 and 80 K and then rise as T goes to 350 K. There is a great deal ofscatter, especially for T > 150 K, but this is to be expected since the dependence of �Tad

on T/C was based on the assumption that �SM values are equal, and from the data presentedin figure 3 this is far from being correct, and secondly the C/T dependence will also depend


on D. The major problem is that the materials which have large �Tad values above 200 Kare FOMT compounds and the �SM values are much greater than those for the SOMT alloy(figure 3). So if one ignores the FOMT data points and concentrates on the SOMT data points1–4 and 25–30 for T > 230 K there is a slight increase in �Tad with increasing temperatureas predicted. At a low temperature, below 230 K, there is a paucity of SOMT data points andone cannot come to any valid conclusions, but the high �Tad value for ErAl2 (point 31) isconsistent with the thermodynamic model.

10.5. The relationship between the magnetoresistance and the MCE

Recently Rawat and Das [72] noted the striking similarity between the temperature dependenceof the magnetoresistance, MR, and the MCE. In a study of the MR and MCE of TmCu andTmAg the authors showed that in spite of the fact that TmCu undergoes an FOMT and TmAgan SOMT, the �ρ(H) versus T (where ρ is the resistivity) and �SM versus T curves for�H = 80 kOe for both compounds are nearly identical and, if properly scaled, lie on top ofone another for the respective compound. A low temperature minimum at ∼7 K in TmCu and∼5 K in TmAg, and a high temperature maximum at ∼9 K in TmCu and ∼10 K in TmAg areobserved in both plots. Also, they point out that �SM has a H 2 dependence in the paramagneticstate due to the suppression of spin fluctuations which is similar to that observed in �ρ(H).This is an interesting observation, and more thought needs to be given to this relationship, boththeoretically and experimentally.

11. Magnetic refrigeration

Magnetic refrigeration came of age on February 20, 1997 in Madison, Wisconsin when theAmes Laboratory/Astronautics Corporation of America (AL/ACA) unveiled their near roomtemperature reciprocating magnetic refrigerator (MR) which had a cooling power of 600 Win a 50 kOe magnetic field over a 10 K temperature span (the temperature difference betweenthe hot and cold heat exchangers), a coefficient of performance (COP) of 10 and a Carnotefficiency approaching 75% [9]. The refrigerator used 3.0 kg of commercial grade Gd spheres.This COP greatly exceeded that of the common vapour cycle refrigerator in use today (i.e.COP = 2 to 4). Since then, eight more near room temperature MRs have been constructedand tested, see below.

The developments that occurred prior to 1997 which led to this breakthrough can befound in several recent reviews [5–7] and will not be summarized here. In addition to a briefsummary of the known existing near room temperature (298 K) MRs, the current status ofthermodynamic refrigeration cycles, magnetic refrigerant regenerator materials and magneticarrays is reviewed in the following subsections. The reader is also referred to several otherreviews concerning some of the pre-2000 research and development work on these topics[6, 12, 13, 20, 228].

11.1. Magnetic refrigerators

Most of the work in the past seven years has been devoted to the 298 K MRs, but someresearch is also being carried out on MRs which operate at liquid H2 (20 K) and liquid He(4 K) temperatures. The former is of interest for the utilization of MRs in the hydrogeneconomy, while the latter is of interest in space applications.

11.1.1. Near room temperature magnetic refrigerators. A brief summary of the operational298 K MRs is presented in table 7. The first machine listed is the proof-of-principle MR which

Recentdevelopm

entsin

magnetocaloric

materials

1525

Table 7. Room temperature magnetic refrigerators.

Max. Max.Announcement cooling Max. magnetic Regenerator

Name Location date Type power (W) �T (K) fielda (kOe) material Ref.

Ames Laboratory/ Madison, Wisconsin, USA 20 February 1997 Reciprocating 600 10 50 (S) Gd spheres [9]Astronautics

Mater. Science Institute Barcelona, Spain May 2000 Rotary ? 5 9.5 (P) Gd foil [229]Barcelona

Chubu Electric/Toshiba Yokohama, Japan Summer 2000b Reciprocating 100 21 40 (S) Gd spheres [230]University of Victoria Victoria, British July 2001 Reciprocating 2 14 20 (S) Gd & Gd1−xTbxL.B.c [231, 232]

Columbia CanadaAstronautics Madison, Wisconsin, USA 18 September 2001 Rotary 95 20 15 (P) Gd spheres [233]Sichuan Inst. Tech./ Nanjing, China 23 April 2002d Reciprocating ? 23 14 (P) Gd spheres; [234]

Nanjing University Gd5(Si, Ge)4pwdr.e

Chubu Electric/Toshiba Yokohama, Japan 5 October 2002f Reciprocating 40 27 6 (P) Gd1−xDyxL.B.c [235]Chubu Electric/Toshiba Yokohama, Japan 4 March 2003 Rotary 60 10 7.6 (P) Gd1−xDyxL.B.c [235]Lab. d’Electrontechnique Grenoble, France April 2003 Reciprocating 8.8 4 8 (P) Gd foil [236]

Grenoble

a Magnetic field source: S, superconducting magnet; P, permanent magnet. b Local announcement only. c L.B. = layered bed.d Privately to KA Gschneidner, Jr.; publicly March 4, 2003. e Actual composition Gd5(Si1.985Ge1.985Ga0.03). f Electric Industry News, October 5, 2002.


demonstrated that magnetic refrigeration is a viable cooling technology which is competitivewith conventional gas compression refrigeration. It ran 8 h a day, 5 days a week, loggingin over 1500 operational hours over an 18 month period without any major maintenanceor repairs, indicating that it was a robust apparatus. The third machine on the list (ChubuElectric/Toshiba [CE/T]) was a modified version of the AL/ACA refrigerator, and the formerhad similar performance parameters considering the Japanese used a smaller amount of Gd anda lower magnetic field. This was an important development since it showed that the AL/ACArefrigerator was not a fluke.

The University of Victoria refrigerator showed that the operational frequency could beincreased by nearly ten-fold from 0.167 Hz (for the AL/ACA and CE/T apparati) to 1 Hz[231]. They also confirmed that the refrigeration power could be improved by using a layeredregenerator bed with two materials with different TCs [232].

The Astronautics Corporation of America’s second refrigerator (called a laboratoryprototype MR) was a much smaller device than their first machine. It is a rotary deviceusing a C-shaped permanent magnet to generate the field (see figure 12(a)). It achieved a noload cooling power of 95 W running at a frequency of 4 Hz. It was put on public display onMay 1, 2002 at the Global Eight (G8) Energy Ministers meeting in Detroit, Michigan. ThisMR runs on a 6 V motorcycle battery, and it can run continuously for 6 h before the batteryneeds recharging.

The Sichuan/Nanjing cooling apparatus was the first refrigerator to use a GMCE material,the Gd5(Si1.985Ge1.985Ga0.03) alloy, as an AMR magnetic refrigerant in an MR. The temperaturespan could be increased over that of Gd by 1 K.

The CE/T team built two more MRs. The first was a reciprocating device using a permanentmagnet to generate the magnetic field, while the second MR had four stationary regeneratorbeds on the circumference of a circle with a rotating bar magnet inside the circle to generatethe magnetic fields as it passed by the beds (see figure 12(b)).

The two European MRs (Materials Science Institute Barcelona [MSIB] and Laboratoirede Electrontechnique de Grenoble) both used Gd foil as the magnetic refrigerant, while all theother seven MRs used various powders. Both teams used permanent magnets: the Barcelonagroup used two bar magnets parallel to one another to generate the field between them, whilethe Grenoble group used a Halbach magnetic cylinder. Furthermore, the MSIB’s MR usedolive oil as the heat transfer fluid.

11.1.2. Low-temperature magnetic refrigerators. Yayama et al [237] proposed a new hybridcryogenic refrigerator which combined a Brayton magnetic cooling cycle with a commonGifford–McMahon (GM) gas cooling cycle. They evaluated the cooling power of the MR withan ErNi magnetic regenerator using a numerical simulation technique with the hot and coldreservoirs at 30 K and 4 K, respectively. They concluded that this hybrid MR has a significantlyhigher refrigeration power compared with a conventional GM cryocooler.

The design of a 0.1 ton/day hydrogen liquefier MR was described by Zhang et al [238].Their analysis showed that the efficiency of a two stage MR operating between 77 and 20 Kwas comparable with that of large (5–20 tons/day) gas cycle liquefaction plants. The smallhydrogen liquefaction MRs are expected to play an important role in the hydrogen economy.

11.2. Thermodynamic cycles

There are a number of thermodynamic cycles which have been utilized in magnetic cooling:AMR, Ericsson and Stirling. The AMR cycle has received the most attention, especially fornear room temperature applications.


(a)

(b)

Magnetocaloricwheel

Permanentmagnet

Cold heatexchanger

Hot heatexchanger

Figure 12. (a ) The Astronautics Corporation of America rotary magnetic refrigeration (right) anda schematic representation of the device (left). A 14 kOe magnetic field around the magnetocaloricwheel filled with Gd spheres is produced by a permanent magnet. The refrigerator operatesnear room temperature with a maximum temperature span of ∼20˚C with a maximum coolingpower of 95 W and operates at a frequency between 1 and 4 Hz. The photograph is courtesyof Astronautics Corporation of America, Inc., Milwaukee, Wisconsin. (b) The Chubu/Toshibarotary magnetic refrigerator (right) and a schematic representation of the device (left). The 7.6 kOepermanent magnet rotates inside of the four magnetocaloric beds, stopping momentarily to allow theappropriate fluid flows to occur before it moves to the next pair of beds. The beds contain Gd–Dyspheres of different Gd : Dy ratios. Using an alcohol water solution as the heat transfer fluid acooling power of 40 W was obtained at a frequency of 0.28 Hz. The photograph and schematic iscourtesy of Chubu Electric Power Co., Inc., Nagoya, Japan.

11.2.1. Active magnetic regenerator cycle. The early (1978) evaluation of the Stirling cyclefor magnetic refrigerators and heat engines by Steyert [239] played an important role inthe development of the AMR concept. The seminal paper [240] (and patent [241]) on theAMR cycle for MR was presented by Barclay at a NASA conference in 1983 [240]. Heshowed that one can get much larger temperature lifts than just the �Tad of the magneticrefrigerant by using the magnetic material simultaneously as a regenerator and the activemagnetic component. Chen et al [242] evaluated a number of thermodynamic cycles (Carnot,


Ericsson, Stirling and AMR) for 298 K MRs and concluded that the AMR cycle is the mostefficient one.

For many years the conventional wisdom held that the ideal temperature profile of themagnetic refrigerant, �Tad versus T , should be a linear function of the absolute temperature[243], but several years ago Hall et al [244] showed that this approximation was incorrect.They also showed that there is no unique �Tad versus T profile for an idealized AMR MR.Furthermore, acceptable profiles must satisfy boundary conditions on �Tad at the hot and coldends of the regenerator as well as an integral constraint on the total magnetic work input. Theyshowed that a convex temperature–distance profile results in minimized entropy generation inthe AMR. These ideas were subsequently tested in an AMR test apparatus a few years later[231, 244]. In the most recent paper Rowe and Barclay [245] conclude that an ideal reverseBrayton-type magnetic cycle cannot be achieved using magnetic materials which undergo aSOMT, i.e. using such a cycle results in entropy generation.

In addition to Barclay’s early work [240, 241] on using the AMR cycle for subliquid N2

temperature refrigeration, several papers dealing with the AMR cycle for hydrogen [243, 246]and helium [243, 247] liquefaction have been published. The basic refrigeration design andmodelling for cooling to 4 K from 80 K, and experimental verification, was reported byDeGregoria et al [243]. More details on the modelling of a hydrogen liquefier were given byDeGregoria [246], while those of a helium liquefier were presented by Johnson and Zimm [247].

11.2.2. Ericsson and other cycles. The temperature–entropy relationship in the ideal Ericssoncycle for magnetic cooling requires that �Tad be a constant over the temperature span betweenthe hot and cold ends of the magnetic regenerator. The effect of heat transfer on the performanceof an Ericsson MR was studied theoretically by He et al [248]. These authors developed theoptimum relationships between the cooling rate and the COP, and between the power inputand the COP of an ideal Ericsson magnetic refrigerant using the basic heat transfer laws andthe Curie law. In another theoretical study, von Ranke et al [66] calculated the MCE of anumber of RNi2 (R = Nd, Gd, Tb, Dy, Ho and Er) intermetallic compounds. They suggestedthat a composite sample consisting of approximately equal amounts of TbNi2 + DyNi2 +ErNi2 would make a suitable Ericsson cycle AMR refrigerant for the 7–22 K temperaturerange.

Annaorazov et al [249] proposed a scheme for a heat pump using FeRh (TC ∼= 300 K) asthe active magnetic material. FeRh undergoes a first-order antiferromagnetic to ferromagnetictransition upon heating, which results in a negative MCE, i.e. �Tad = −12.9 K for �H =19 kOe. The calculated heat transfer for 5 and 10 K temperature spans and a magnetic fieldchange of 25 kOe suggest that FeRh would be an effective magnetic refrigerant near roomtemperature [249]. Unfortunately the cost of Rh ($20 000 per kilogram) puts this materialoutside the realm of a commercial device, but nevertheless it is a scientifically interestingmaterial.

11.3. Regenerator materials

Gadolinium metal is considered the prototype magnetic refrigerant material for the 298 K MRs.It is a good refrigerant, but to make magnetic refrigeration even more efficient, it is necessaryto find new materials with better MCE properties than Gd. Of course, there are other ways toimprove the efficiency, but in this review we are only concerned with the magnetic refrigerant.Since the discovery of the GMCE in Gd5(Si1−xGex)4, see section 5, a number of materials havebeen proposed as substitutes for Gd. These include the manganites (section 8), Mn(As1−xSbx)

alloys (section 6.1), MnFe(P1−xAs) alloys (section 6.2), the Ni∼2Mn∼1Ge∼1 Heusler alloys


(section 6.3) and La(Fe13−xMx)-based materials (section 7). In the following subsections wehave evaluated these materials as magnetic refrigerants and discussed large scale productionand some special effects.

11.3.1. Evaluation of magnetic refrigerant materials. The most common method usedby scientists and engineers to compare MCE materials is to use �SM values, which areusually reported in mass units (J kg−1 K−1), of material ‘X’ with Gd. However, these arethe wrong units for making such a comparison since the engineer designing the MR wantsthe largest entropy change in the smallest possible volume, i.e. the largest cooling power percubic centimetre. For this reason we have converted all the �SM values in this review tomJ cm−3 K−1 units. A comparison of the �SM values for many of the magnetic refrigerantcandidate materials is found in figure 3.

A second problem with comparing �SM values is that the �Tad value is not taken intoaccount. A better parameter for comparing magnetic materials is the refrigerant capacity,which is defined as

q =∫ T2

T1

�SM(T ) dT , (6)

where T1 and T2 are the temperatures of the hot and cold sinks, respectively, and �SM(T ) is therefrigerant’s magnetic entropy change as a function of temperature. The refrigerant capacity,therefore, is a measure of how much heat can be transferred between the cold and hot sinks inone ideal refrigeration cycle.

In figure 13 we plot q versus TC for many of the materials discussed in this review.Generally the temperature dependence of �SM is not known and so the reported values of q arelimited, especially when compared with �SM. As noted, most of the materials with TC ∼= 298 Khave q values which are slightly higher than that of Gd. As might be expected, q increases withdecreasing temperature for the same reason that �SM shows the same temperature dependence,see section 10.4.1.

Another common mistake is that many times the TCs of the two materials being comparedare more than 25 K apart, and such a comparison is not valid since �SM has a strong temperaturedependence as discussed in section 10.4.1. The same is true for q.

The cost of the raw materials is generally stated to be an advantage of material ‘X’, becauseGd is thought to be rather expensive. This is probably correct in many instances. But what isneglected in most cases is the other costs involved in preparing large quantities (>1 kg) of therefrigerant materials on a production basis and in fabricating this material into a useful formto be used in the AMR regenerator beds—spheres, wires, screens, foils, etc—and thus thecompetitive advantage may be quickly lost. For most of the candidate magnetic refrigerants,namely the manganites, La(Fe13−xSix), Mn(As1−xSbx), MnFe(P1−xAsx) and Ni∼2Mn∼1Ge∼1

Heusler alloys (see sections 8, 7.1, 6.1, 6.2 and 6.3, respectively, for more details on samplepreparation), these materials have only been made on a small scale, 5–25 g, and generallythere are long-term anneals (�24 h), sometimes more than one annealing step, necessaryto homogenize the sample. When MRs are mass produced, tons of magnetic refrigerantper day will be required; and the factory space and amount of high temperature vacuumequipment to carry out such annealing processes will be vast and require an extremely largecapital investment, much more than what is needed for preparing Gd metal and Gd5(Si1−xGe)4

(see section 11.3.2). Since most of the magnetic refrigerant materials are inorganic compoundsor brittle intermetallic compounds, these materials will be difficult to fabricate in high-efficiency forms—wires, screens or foils. On the other hand, Gd is a ductile metal and can be,in comparison, easily fabricated into these forms.


∆∆ ±

Figure 13. The refrigeration capacity, q, as a function of the Curie temperature for a fieldchange of 50 kOe, with T1 = TC − 25 K and T2 = TC + 25 K (see equation (6)) forthe RCo2, RAl2, R5(Si1−xGex)4, MnFe(P1−xAsx) and La(Fe13−xSix) families and Gd metal(the prototype AMR material), plus a few other intermetallic compounds and alloys. Some ofthe q values [RCo2 phases and some of the Gd5(Si1−xGex)4 compounds] are unpublished valuesof the authors.

Compound legend1—Gd5.00Si4.00

2—Gd5Si3.00Ge1.00

3—Gd5Si2.30Ge1.70

4—Gd5Si2.10Ge1.90

5—Gd5Si2.02Ge1.98

6—Gd5Si1.98Ge2.02

7—Gd5Si1.80Ge2.20

8—Gd5Si1.60Ge2.40

9—Gd5Si1.50Ge2.50

10—Gd5Si1.30Ge2.70

11—Gd5Si1.01Ge2.99

12—Gd5Si0.64Ge3.36

13—Gd5Si0.50Ge2.50

14—Gd15—MnFeP0.65As0.35

16—MnFeP0.55As0.45

17—MnFeP0.50As0.50

18—MnFeP0.45As0.55

19—MnFeP0.65As0.35

20—DyNi221—DyAl222—GdAl223—Gd0.85Er0.15

24—LaFe11.7Si1.3

25—La(Fe0.99Mn0.01)11.7Si1.3

26—La(Fe0.98Mn0.02)11.7Si1.3

27—La(Fe0.97Mn0.03)11.7Si1.3

28—La(Fe11.44Si1.56)

29—La(Fe11.44Si1.56)H0.5

30—La(Fe11.44Si1.56)H1.0

31—La(Fe11.44Si1.56)H1.5

32—ErCo2

33—HoCo2

34—DyCo2

35—TbCo2

Another problem with the intermetallic Mn refrigerants containing As and/or P is the factthat both have high vapour pressures (the boiling point of As is 876 K and that of P is 550 K).This makes the handling of these elements in the production of the appropriate compound anadditional challenge and will add additional costs in manufacturing the magnetic refrigerantalloy. Most developed countries have strict environmental regulations, and thus enormousinvestments will be required to ensure triple or even quadruple redundancy in safety, thuseliminating potentially devastating accidents releasing As and/or P into the environment.

Environmental concerns associated with As, P and Sb, all of which are poisons,complicates matters because alloys containing these elements will require special handlingfacilities, assuming that the various governmental health and environment agencies around theworld allow these elements to be utilized in magnetic refrigerant regenerators. We estimate thathousehold cooling appliances will require on the average hundreds of grams of the magneticrefrigerant.

Recently Provenzano et al [250] reiterated the well-known notion that hysteresis might bea problem for magnetic refrigerant materials which exhibit the GMCE because of the first-order


Table 8. The hysteresis associated with the first-order GMCE mangetic transition in the materials.

�H Type ofCompound �T (K) Ref. (kOe) Ref. transformation

DyCo2 — — 2 [36, 38] IEMHoCo2 — — 3 [36, 38] IEMErCo a

2 — — 5 [38] IEMErCo b

2 — — 11 [40] IEMGd5(Si2Ge2) 2–14 [167] 10 [167] MagnetostructuralMnAs 6.5 [127] — — MagnetostructuralMnFe(P1−xAsx)

0.25 � x � 0.65

}4 [88] 7 [88] Magnetostructural

Ni54.8Mn20.2Ga25.0 7 [139] — — MagnetostructuralLa(Fe11.44Si1.56) 3 [162] 5 ± 1 [141, 162] IEM

a Polycrystalline sample.b Single crystal, [111] parallel to H .

magnetic/structural transition. Even though in general this may be correct, it still remains tobe demonstrated that one cannot utilize a particular GMCE material in an MR. Indeed, asnoted in section 11.1.1, the Chinese [234] have successfully utilized a Gd5Si1.975Ge1.975Ga0.03

GMCE material in an MR, and its performance was slightly better than that obtained usingSOMT Gd under the same conditions and in the same MR. The amount of hysteresis forsome of the candidate magnetic refrigerant regenerator materials is summarized in table 8. Itis noted that as a whole the hystereses are larger for the four compounds which undergo amagnetic/structural FOMT as compared with those which exhibit an FOMT due to IEM. Thus,if hysteresis is a problem, it would be the worst for the Gd5(Si1−xGex)4 compounds, slightlyless for the three Mn-based alloys and the least for La(Fe11.44Si1.56) and the RCo2 phases.

Of even greater concern is not the hysteresis of the FOMTs, but the time dependence of�Tad, see section 10.1. In the case of Gd5(Si2Ge2) and La(Fe11.44Si1.56) the directly measured�Tads are significantly smaller than those obtained indirectly from heat capacity measurementsbecause of the kinetics of the transformation—the more rapidly �Tad is measured the smallerthe value of �Tad, by 30–50%. This could be a real problem because MRs will operatebetween 1 and 10 Hz and much of the MCE will be lost (i.e. not utilized) during the magneticfield increase and the field decrease. How much of the MCE is not utilized in one cycle remainsto be determined. Nothing is known about the time dependence of �Tad for the manganites,which exhibit an FOMT, and the Mn(As1−xSbx), MnFe(P1−xAsx) and Heusler alloy families,but it is reasonable to expect they will exhibit similar behaviours. As noted in section 10.1,there is no time dependence for Gd metal.

Corrosion may be a problem since a water-based solution is used as the heat transfer fluidin most MRs built to date. Gd spheres have been successfully used in several MRs and nocorrosion has been reported in any of the reports on the operational results of these devices.As a matter of fact, the Gd spheres used in the AL/ACA proof-of-principle apparatus are stillas shiny after 1500 h of operation as when they were loaded into the MR. The Gd5(Si1−xGex)4

alloys are much more stable to oxidation (no measurable weight gain in air at 123˚C over a fivemonth period) and corrosion (no evidence of a reaction of the powders with tap water) thanGd metal [251]. The La(Fe13−xSix) alloys may suffer some corrosion problems, since all thesamples prepared to date contain α-Fe (see section 7). No information is available concerningthe compatibility of the manganites and the three Mn-based intermetallic compounds withwater, but they all seem to be stable in ambient (humid) air, which suggests aqueous corrosionmay not be a problem.


Table 9. Advantages and disadvantages of various magnetic refrigerants.

Factor Gd Gd5T4 RMnO3 LaFeSi MnAs FeMnPAs Ni2MnGa

Raw material costs 0 − ++ ++ ++ ++ +Preparation 0 − −− −− −− −− −−Vapour pressure 0 0 0 0 −− −−− 0Fabrication (sheet) 0 − − − − − −MCE, |�SM| 0 ++ − + + + +MCE, �Tad 0 + − − − − ?Refrigeration capacity 0 + ? + ? + ?Hysteresis 0 −− 0a − − − −Time dependence of �Tad 0 − ? − ? ? ?Environmental concerns 0 0 0 0 — — 0Corrosion 0 ++ ? − ? ? ?

a For SOMT manganites; for the few FOMT maganites the zero becomes a minus.

The advantages and disadvantages of the candidate magnetic regenerator materials aresummarized in table 9. The comparison is made with Gd metal, the prototype magneticrefrigerant. A zero indicates that the factor is essentially the same as for Gd; a plus means thatthe behaviour is somewhat better than Gd, and two pluses mean it is much better. A minussign indicates that the property is inferior to that of Gd, and two or three minus signs indicatethe behaviour is much worse, or much more worse than for Gd. Most of the properties havebeen discussed in the above paragraphs of this subsection, while the �SM, �Tad and q valuesare found in figures 3, 4 and 13, respectively. It is seen that there is no clear favourite GMCEmaterial as a replacement for Gd and Gd-based solid solution alloys, Gd–R. As a matter offact Gd and its solid solution alloys do well in holding their own as the near room temperaturemagnetic refrigerant of choice as of today.

11.3.2. Large scale production. There has only been one investigation of developing a methodfor the large scale production of magnetic refrigerant regenerator materials. Gschneidneret al [103, 252] described a kilogram scale process for manufacturing the Gd5(Si1−xGex)4

alloys from commercial grade Gd metal. The major obstacles overcome in making ahigh-quality product were the finding of a suitable crucible material (Ta) for reacting thecomponents and melting the refractory Gd5(Si1−xGex)4 alloy (the melting point exceeds1750˚C), and the developing of a heat treating protocol for reducing the carbon impurity fromthe Gd starting material and minimizing the eutectoid transformation of the monoclinic formto the orthorhombic modification between 400˚C and 700˚C. Over 10 kg of the Gd5(Si2Ge2)

material with good GMCE values, two-thirds of that prepared by arc-melting using high-purityGd, was produced.

As far as we are aware no other study has been made to prepare large scale quantities ofother AMR regenerator materials.

11.3.3. Special effects. Luo et al [253] developed a method for fabricating porous monolithicregenerator forms starting with fine powders of the magnetic refrigerant material. Theregenerator bed was prepared by bonding the ∼230 µm powders using a low-temperatureepoxy. Several single layers and multilayer beds with porosities of ∼0.39 were prepared andtested with good results. The authors claim their technique is a cost effective way of fabricatingefficient magnetic regenerators.

Lewis et al describe a simple way of improving the MCE in ferromagnetic materials bycoating slices of the GMCE Gd5(Si1.5Ge2.5) with pure Fe [115] or Al [116]. The coating layers


were 0.1 and 0.2 µm thick for Fe and 0.1 µm for Al. The 0.1 µm Fe coating increased theGMCE by ∼11%, while the 0.2 µm coating had no appreciable difference in the effect. TheAl coating improved the GMCE by 20%. The enhancement was thought to be due to a strainthat the coatings imparted on the Gd5Si1.5Ge2.5 particles.

11.4. Permanent magnet arrays

An important aspect of magnetic refrigeration is the magnetic field source, since the efficiencyscales directly with magnetic field. For large scale applications, e.g. building climate control,supermarket chillers, refrigeration plants, etc, superconducting magnets will be utilized withoutlosing the efficiency associated with the need to use liquid helium or a cryocooler to maintaina superconducting magnet close to 4 K. But for household and automotive applications,superconducting magnets are out of the question and we will have to rely on permanent magnetsat least in the foreseeable future. Thus the design of high-field, low-cost permanent magnetarrays for magnetic refrigeration is an important aspect of the commercialization of MRsin the consumer market. Several recent papers have addressed this problem. Lee and Jiles[254] describe geometrical enhancements to permanent magnet flux sources. Their designgenerated a magnetic field of 30 kOe in a 1.52 cm gap. Tang et al [255] presented a descriptionof a permanent magnet circuit with an air gap. Their optimum magnet array had a flux of8.2 kOe in a gap of 1.5 cm. Xu et al [256] described the design of a 16 piece hollow cylindricalpermanent magnet array. They also calculated the effect of cutting a slot (10 cm) in this array toallow the magnetic refrigerant to enter and exit the magnetic field. However, no field strengthswere given for their design.

12. Conclusions and summary

Over the past seven years there has been an upsurge in our knowledge of the MCE and manymaterials have been investigated for their MCE properties. A number of new materials withGMCE properties have been discovered and proposed as viable magnetic refrigerants. TheMCE properties of the best magnetic materials have been compared. However, there is noclear winner as a replacement for Gd metal, the prototype 298 K magnetic refrigerant material.As of today, Gd and Gd-based solid solution alloys are still the materials of choice.

Acknowledgments

We thank Mr Lucas Hale and Drs Zhongwen Ouyang and Durga Paudyal for their assistancein producing this review, and Mrs Carol Smith for typing most of the original manuscript. Theauthors wish to express their appreciation to Drs Steve Russek (Astronautics Corporation ofAmerica, Inc., Milwaukee, Wisconsin, USA) and Hirano Naoki (Chubu Electric Power Co.,Inc., Nagoya, Japan) for furnishing the photographs and schematics of their rotary magneticrefrigerator. This work was supported by the Office of Basic Energy Sciences, MaterialsSciences Division of the US Department of Energy under contract No W-7405-ENG-82.

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